Is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B working together they can do it in *?

Discussion :: Time and Work - General Questions (Q.No.4)

A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:

[A].	20 days
[B].
[C].	25 days
[D].	30 days

Answer: Option B

Explanation:

Ratio of times taken by A and B = 1 : 3.

The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.

If difference of time is 2 days, B takes 3 days.

If difference of time is 60 days, B takes		3	x 60		= 90 days.
2

So, A takes 30 days to do the work.

(A + B)'s 1 day's work =		1	+	1		=	4	=	2
30	90	90	45

A and B together can do the work in	45	= 22	1	days.
2	2

Rajender said: (Jun 16, 2010)
Please tell me how you have calculated differece of time 2 days.

Sundar said: (Jul 5, 2010)

Hi Friends! The statement "A is thrice as good as workman as B" states that, If A complete a work in 1 day, B will take 3 days to complete the same work. Therefore, if A takes 1 day, B takes 3 days, the time difference is 2 days. If the time difference is 2 days, B takes 3 days to complete the work. Similarly if the time difference is 60 days, then B takes (3/2*60) = 90 days. Then A takes 90 - 60 = 30 days to complete the work.

It is very simple man.

Kumar said: (Jul 5, 2010)

Hi Guys, Let me do the same thing with different values. Given statement : "A is thrice as good as workman as B" Time difference : 60 days. If B takes 12 days to complete a work, A will take only 4 days to complete the same work. So, B takes 12 days whereas A takes 4 days only (because A is thrice as good as B). Here time difference is 12 - 4 = 8 days. If the time difference is 8 days, B takes 12 days. Similarly if the time difference is 60 days, then B takes (12/8 * 60) = 90 days.

...Rest thing you can understand from the explanation part.

Bharathi said: (Jul 9, 2010)
Dear Friends, In this question atlast we got (a+b)'s 1 day work=2/45. How it is changed to be an A and B are together can do the work in 45/2.

Nagu said: (Jul 12, 2010)
Hi Bharathi, If A takes 10 days to complete a work means A's one day work is 1/10 so complete this work A takes 10/1 days is same as 10 days Sat the same way (A + B)'s 1 day's work 2/45 means They will take 45/2 = 22 1/2 days I think you got my point have a nice day

SHEETAL said: (Aug 3, 2010)

Hi Guys, Don't be confused in data given in question. I have one short cut to solve such kind of question. A is K times as good a worker as B & takes X days less than B to finish the work. Then the amount of time required by A & B working together is K * X / K'S SQUARE - 1. SO IN QUESTION K IS 3. X IS 60. SO PUTTING THE VALUES IN ABOVE MENTIONED FORMULA. K * X / K'S SQUARE - 1 =3 * 60 / 9 - 1 =3 * 60 / 8 =180 / 8 =22.5 DAYS AS MENTIONED OPTION B. I HOPE U WILL UNDERSTAND THIS THING & WILL APPLY IN QUESTION BASED ON THIS.

All the best. Have nice day!

Sangeetha said: (Aug 4, 2010)
Oh thanks sheetal

Indhu said: (Sep 1, 2010)

Hi friends,. Though content is big it is easy to understand. Work done by A as compared to B=3:1. Time taken by A as compared to B=1:3. So, time difference is 2. A will finish the work 60 days lesser than B. Therefore time difference is 60. Time taken for A = 60/2 = 30. Hence time taken for B=3* time taken by A = 90. If A+B can do a piece of work in n days, then (A+B) 's 1day's work=1/n. Working together (A+B) 's one day work = (1/30) + (1/90) =2/45. If (A+B) 's 1day's work=1/n, then A+B can finish the work in n days.

Therefore total time taken = 45/2= 22. 5 Days.

Prashant said: (Sep 15, 2010)
Suppose B takes x days to finish the work and then according to question A will take (60-x) days to work. in question the ratio of time taken is 1:3 therefore 1/3= (60-x)/x x=45 So A can complete the work in (60-x)=(60-45)=15 days So (A+B) one day's work =(1/15 + 1/45) =4/45 So (A+B) complete the work in 45/4 = 11 1/4 days.

Sugumaran said: (Sep 22, 2010)
Ratio of time taken=1:3 A finish the work in 60 days and B in x days. 1:3::60:x x=180 days So, A and B 1'days work 1/60+1/180=45 days Is it correct or not?

M.Atul said: (Sep 23, 2010)
@Sugumaran please read carrefully problem. Though you have got same answer but it doesn't satisfied second condition that differnce in day should be 60 not 120.

Priya said: (Sep 23, 2010)
Please tell me why we are taking 3/2 to multiply with 60. Please explin me.

Harsha said: (Oct 13, 2010)

A clear approach: Given: A's time taken:B's time taken=1:3 So A's proportion of time taken=1/(1+3)=>1/4*some x B's proportion of time taken=3/(1+3)=>3/4*some x As it is said that difference of time is 60 days B's time-A's time=60 => 3x/4-x/4=60 =>x=120 So A's proportion of time taken =x/4=120/4=30 days B's proportion of time taken =3x/4=3*120/4=90 days A's 1 day's work = 1/30 B's 1 day's work = 1/90 (A + B)'s 1 day's work = (1/30 + 1/90)= 4/90=2/45

A and B together can do the work in 45/2 = 22 1/2 days.

Naveen said: (Oct 26, 2010)
Hi, in prashanth answer, he equals the ratio 1/3 to 60-x/x but it actually x-60/x.

Shilpi said: (Nov 18, 2010)
Can you pls teach me this equation 1/30+1/90=4/90

ASHIRWAD said: (Nov 27, 2010)
HI FRIENDS THIS IS THE simplest method for solving this type of que.... K*S/(A^2-1) where S=DAYS FOR FINISHING WORK(60 GIVEN IN QUE) K=3 GIVEN IN QUE

Ashirwad Dubey said: (Nov 28, 2010)
Hi friends k*x/(k^2-1) k=3 x=60 given in que ok friends

Vikas said: (Dec 29, 2010)
I didnt understand how did we get that (3/2)*60 ?

Showry said: (Jan 5, 2011)
Hi Friends, A:B=1:3 time taken.........since A is 3 good as B A takes 60 days less than B B-60:B=1:3............ i.e B-60/B=1/3..... B=90 days.... A=30...... (A+B)'s one day work (1/30+1/90) = (2/45) Total work by (A+B) is 45/2 i.e 22 1/2.............

Gowri said: (Jan 8, 2011)
kl/(k)^2-1 k=3 l=60 3*60/(3)^2-1 =45/2 =22.5

Nagarjun said: (Jan 13, 2011)
@Vikas Its just cross multiplication. If the difference is 2 days then b takes 3 days If the difference is 60 days then b takes x days Hence, x= (60*3)/2. I think you got it now.

Naresh Kumar said: (Jan 18, 2011)
Thank you guys.

Malini said: (Jan 19, 2011)
Sheetal thanks a lot dear. This short cut is very much easy.

Baskar said: (Jan 21, 2011)
@bharathi i think u r in confusion.. just know dat work = day.. 1 day = 2/45 works.. in ques ask abt "work"? den cross mul 1 work = 45/2 days.. now u got it

G.P. said: (Feb 10, 2011)
SIMPLE AND BEST WAY since a is thrice better than b hence a:b=1:3 similarly a takes 60 days less than b hence a:b=(b-60):b=1;3 cross multiplication n we get 3b-180=b hence b=90days hence a=30days 1/90+1/60=4/90 hence total daysreciprocal 90/4=45/2

Nishant said: (Feb 10, 2011)
@ G.P. Thanks. I like the way you solve it.

Balaji said: (Feb 19, 2011)
Showry you explained superbly.

Prathyusha said: (Feb 28, 2011)
SIMPLE AND NICE EXPLANATION!... @KUMAR

Vani said: (Mar 18, 2011)
Showry's explanation is good.

Siva said: (Apr 21, 2011)

Hi Guys, I think following simple method (alternate) will make you more clear, A can complete work in N days => A's 1day work = (1/N)----1 B can complete work in n days => B's 1day work = (1/n)----2 Given data, A thrice as B so , A=3B A complete work 60 days less than B so, (N=n-60) Apply in 1 & 2 A's 1day work = (1/(n-60))-----3 B's 1day work = (1/n)--------4 we know that A=3B ; B=(1/n) so,Apply B in A we get[A=3/n] Apply in 3 3/n=(1/(n-60)) by solving, 3n-180=n n=90 so, B can complete work in 90 Days => B's 1 Day work =(1/90) we know that N=n-60, so, A can complete work in 30 Days => A's 1 Day work = (1/30) (A+B) 1 Day work = (1/30 + 1/90) by solving we get, A+B 1 Day work = 2/45,

so A and B together can complete work in 45/2 Days.

Hindu said: (Jun 25, 2011)
Hai sheetal your shortcut method helps lot to understand so quickly its really super.

Naveen Kumar said: (Jul 1, 2011)

Hi friends, Here is a simple technique to calculate the above problem.... Given, If the If difference of time is 2 days, B takes 3 days. If difference of time is 60 days, B takes......? We can represent the above relation like this, 2------->3 60------>....? By cross multiplying the above terms we will get... 60*3/2 = 90. Note:- Always individual term should come in the denominator. By applying the above procedure you can solve any problem of this type....

I think this technique will help you while doing with this type of problems...

Abdul said: (Jul 9, 2011)
Hey Siva your way of solving is fantastic and understandable! Thanks.

Jezan said: (Jul 17, 2011)
According to this question if A is x, B will be x+60 1/3=x/x+60 3x=x+60 2x=6 x=30 A+B'S ONE DAY WORK=1/30+1/90=2/45 SO WHOLE WORK S= 45/2( UPSIDE DOWN) 22.5 DAYS. HOPE ALL LL GET DIS

Jaswinder Singh said: (Aug 14, 2011)
Ratio of times taken by A and B = 1 : 3. or 1x:3x so, we say 3x-1x=60, 2x=60, x=30, so A will 30 day to complected a work, B will be complete the work ie 3x, 3(30)=90days, (A+B) 1 Day work = (1/30 + 1/90) by solving we get, A+B 1 Day work = 2/45, so A and B together can complete work in 45/2 Days.

Sharan said: (Aug 21, 2011)
@Jaswinder singh: I understood your explanation man. Thanks.

Sundar said: (Aug 22, 2011)

@All (Must read if you have any doubts) If B takes 3 days then A takes 1 day to complete the task. Time taken Ratio => A : B = 1 day : 3 days. 1 3 (difference is 2) 10 30 (diff 20) 30 90 (diff 60) <= Here diff is 60 days, So this is the correct ratio to be used in calculation, since it was mentioned in the given question. A alone can finish the task in 30 days. B alone can finish the task in 90 days. Work done by A alone in 1 day = 1/30 Work done by B alone in 1 day = 1/90 Work done by A and B in one day (1/30 + 1/90) = 3+1/90 = 4/90 The no. of days required to complete the task by A and B is = 90/4 = 22.5 days. ////**** Important Note: ****//// We cannot take other ratios like 1:3, 10:30, 40:120, 60:180 for the calculation. Since the diff is mentioned as 60 days. Because, it will give different answers for each different ratios used for calculation. If we take 1:3 => (1/1 + 1/3) = 4/3 If we take 10:30 => (1/10 + 1/30) = 4/30 If we take 40:120 = (1/40 + 1/120) = 4/120 If we take 60:180 => (1/60 + 1/180) = 4/180 ... so on.

I hope this will help you. Have a nice day!

Deepti said: (Aug 25, 2011)
It is not so big and easy to understand. let work done by B in 1 day = 1/x so work done by A in 1 day = 1/(x-60) 1/(x-60) = 3/x so x = 3x - 180 x = 90 work done by A and B in 1 day is 30 and 90 respectively work done by both together in 1 day = 1/30 + 1/90 = 2/45. total work done = 45/2

Harsha said: (Sep 1, 2011)
Easy method : A can completed in x days B can in 3x days then A = B-60 (A can do in 60 days less than B ) => x=3x-60 => x= 30 => A=30, B=90 Then together work done is (1/30+1/90) = 2/45. Finally total work done is 45/2.

Pinky said: (Sep 10, 2011)
@Sheetal superb explanation.

Praveen said: (Sep 16, 2011)
Nice exp. Harsha.

Nitin Singla said: (Sep 23, 2011)
Hey its simple to understand. Days taken by B = x Days taken by A= x - 60 Their time taken proportio is 1:3 so, x - 60/ x = 1/3 x=90; So A will do the work in = 30 days abd B in 3x= 3*30=90 days, and u can find their 1 day's work and ad it. Simple :)

Srinivas said: (Sep 25, 2011)
Hi friends, Given A:B=1:3 Therefore B=3A--------equation 1 let B can do a work in x days. then A can do the same work in (x-60) days. then B=3A x=(x-60)3 therefore x=90 days therefore B can do a work in 90 days. and A will do a work in 90-60=30 days.

Pavethra said: (Sep 29, 2011)
I tell that A is thrice as good as B so it should be 3:1 na. Am I right?

Sunil Reddy said: (Oct 4, 2011)
We can use a simple formula here:[(KL)/k squqre-1)] -->here K=3(efficiency),L=60(time) so (360/(33)-1)=>180/8=221/2

Vinod Reddy said: (Nov 7, 2011)
THANK U SHEETAL,your short cut method is simply super.there is no words to say

Sundar said: (Nov 18, 2011)
If difference of time is 60 days 3*60/2 = 90 days. I can't get this step? Please explain.

Riyaz said: (Nov 23, 2011)

Ratio of times taken by A and B = 1 : 3. That is If A takes 1 day B takes 3 days Time Difference is 3-1 = 2 days Here is the tricky part : If A takes 1/2 day B takes 3/2 days Time Difference is 3/2 - 1/2 = 1 days When time difference is 60 days (Just mulitply by 60) A takes 60/2 and B takes 3*60/2 So, A takes 30 days to do the work. and B takes 90 days to do the work. A's 1 day's work = 1/30 B's 1 day's work = 1/90 (A + B)'s 1 day's work = (1/30 + 1/90)= 4/90 = 2/45

A and B together can do the work in 45/2 = 22+1/2

Anu said: (Nov 27, 2011)
Awesome explanation HARSHA

Brajesh Anuragi said: (Nov 28, 2011)
Thanks Showry for given the simple and correct ans.

Gauarv said: (Dec 27, 2011)
Thanks harsha.

Neeraj said: (Jan 8, 2012)
A will finish the work 60 days lesser than B. What is it mean please explain?

Abhay said: (Jan 10, 2012)
@Neeraj-A will finish the work 60 days lesser than B,means if B takes 60 days to complete the work,A takes 1 day.

Sureshkumar said: (Jan 19, 2012)

Another easy way 2 find out: 1st put the ratio i.e.1:3(A:B) 2nd the condition given here is A can work less than 60 days So, find out the probability that matches with the ratio condition(A&B must be difference 60 here) for eg:let we take as A as 20 therefore B must be 60(here we get the difference as 40 only)according to 1:3 which cant satisfy The given condition(A less than B by 60 days) suppose you take A as 30 means you get B as 90 which is greater than 60 days of A....A=30 B=90 A's 1 day work=1/30

B's 1 day work=1/90 A+B's 1 day work =1/30+1/90=4/90 here they are not given to find out as 1day work...so take as 90/4=22.5 <==> 22(1/2).

Varma said: (Jan 26, 2012)
Nice formula @Sheetal.

Aarush said: (Feb 16, 2012)
Thanks sheetal.

Raman(UIET,KUK) said: (Feb 17, 2012)
Guys check this out and don't be confused.... as we know A is 3 time better than B and A takes 60 days less than B so, time taken by A: time taken by B= 1:3 = b-60:b ( suppose time by B is b) by cross multiply, 3b-180=b i.e. b=90 so time taken by B=90 and time taken by the A is=90-60= 30

TABISH said: (Feb 18, 2012)
@sheetal do not able to understand how you get that formula to calculate the time i.e. K*X/K^2-1

Kapil said: (Feb 20, 2012)
Nic Explanation. . .Sheethal. . .

Shro said: (Feb 20, 2012)
Indhu very easy simple explanation as per the question. Good :) thanku :)

Sindhu said: (Feb 23, 2012)
HI, This method I feel to be quiet easier. A is thrice as good as workman as B. therfore, A=3B -(1) finish a job in 60 days less than B 1/B=60+1/A -(2) i.e B`s One day work = A`s one day work + 60 days. Solve (1) & (2) we will get A= 90; From (1) B=A/3 => B= 30. (A+B)`s 1 day work = 1/90+1/30 =2/45 =22 1/2 days

Iyappan said: (Apr 12, 2012)
Naveen kumar your explanation is beautiful for me.

Sanchi said: (Jun 3, 2012)
Very simple way. 3A=1B B takes x days. 3 (x-60) =x 3x-x=180 X dats is B=90, A=30. Now, 1/90+1/30=22. 5.

Nitin Singh Parihar said: (Jul 5, 2012)
Let B do the work in 'x' days. So, A will take (x-60) days. Now, ratio of A:B=1:3 (given in ques). So, 1/3=x-60/x. => x=90 (B's 1 day work). So, A's work=30 days. Working together=1/30+1/90. =45/2 days. Easy and simple.

Akansha said: (Aug 7, 2012)
B takes 3 times more days than A. i.e. B=3A. So. B-A=60. 3A-A=60 =>. A=30. B=90. Now calculate 1 day work of A and B.

Sunny said: (Aug 26, 2012)

A is thrice as good as workman as B means 1:3(Ratio) Therefore A is able to finish a job in 60 days less than B So A= 1/60 and B=1/60 .....(Given) According to the ratio A=1/60 B=1/3*60 (As we are calculating by days) So Now A = 1/60 < B = 1/90 (A finishes work less than B) Working together, they can do it in: 1/A+B = 1/60 + 1/90 (As we are calculating by days)) 1/A+B = 2/45 So A+B = 45/2 Days

Option (B) is the correct ans

Vidya said: (Aug 27, 2012)
Can you please solve this using unitary method. Its b'coz I follow that method.

Anji said: (Sep 4, 2012)
Let the time taken by A be x days, then time taken by B will be 3x days. Given that, time taken by A to finish the work = time taken by B -60 i.e, x=3x-60 => x=30. Therefore, time taken by A to finish the work is 30 days. so B takes 90 days. Now ,work done by A & B in 1 day=1/30 + 1/90 =4/90 =2/45 Time taken by A & B to complete the work=45/2 days =22 1/2 days

SANJEEV said: (Sep 11, 2012)
#include<stdio.h> void main() { float a,b; int c,d; printf("enter ratio of A : B\n"); scanf("%f",&a); printf("enter no of days lesser than B by A to complete work\n"); scanf("%f",&b); c=ab/(a-1); d=c-b; printf("no of days to complete work by A and B is %d",(c*d)/(c+d)); }

Prabha said: (Sep 24, 2012)
If difference of time 2 days B takes 3 days Similarly why don't we take difference of time 60 days B takes 60*3 is 180 days. Please explain to me ?

Joshi Sir said: (Nov 21, 2012)

Friends, don't make it complex: Here we go. Ratio of time taken by A & B = 1:3 And A takes 60 days less then B Suppose, days taken by B = x then days taken by A = (x - 60) Thus, A : B = (x - 60) : x 1 : 3 = (x - 60) : x 1/3 = (x - 60) / x X = 3 (x - 60) X = 3x - 180 180 = 3x - x 180 = 2x X = 180 / 2 = 90 Hence, Days taken by B = x = 90 days Days taken by A = (x - 60) = 90 - 60 = 30 days 1 day work of A and B = 1/30 + 1/90 = 4/90 = 2/45 So,

Total days taken by A & B to complete the work = 45/2 = 22.5 days

Ashutosh said: (Nov 29, 2012)
Formula-->nx- (n+1) /nx. 4x-4x/3=60 so x=45/2.

Keerthi said: (Jan 10, 2013)
So by the explanation above we have to take in the ratio 1:3.

Kavya said: (Jan 10, 2013)
A is twice as good a workmen as B and together they can finish a piece of work in 18days. In how many days will A alone finish the work? Can we solve the above problem using the formula k*x/k^2-1.

Pankaj said: (Feb 5, 2013)
Let A takes x days to do the work alone Therefore days taken by b is (x+60). Now A is 3 times faster than B So no.of days taken by A will be 3 times less than B. So 3*x=(x+60) 2x=60 x=30 days //work done by A Work done by B=30+60=90 days. Now we can find work done together 1/30 +1/90 to get the answer.

Monika said: (Feb 11, 2013)
We have a direct formula for these kind of questions .. i.e., Work done together is given by = (md)/(m^2 - 1), Where d is no of days taken by B and m is no of time A is faster than B, Therefore = (360)/(3^2-1) = 22.5.

Praveen said: (Mar 10, 2013)

@All. Please refer to Sheetal's response as given below. Its the best and easiest way to solve such questions. PS:Thanks sheetal. "A is K times as good a worker as B & takes X days less than B to finish the work. Then the amount of time required by A & B working together is K * X / K'S SQUARE - 1. SO IN QUESTION K IS 3. X IS 60. SO PUTTING THE VALUES IN ABOVE MENTIONED FORMULA. K * X / K'S SQUARE - 1 =3 * 60 / 9 - 1 =3 * 60 / 8 =180 / 8 =22.5 DAYS.

AS MENTIONED OPTION B.

Sridhar said: (Apr 28, 2013)
Simple way: A and B ratio 1:3. Since A finishes 60 days lesser than be A takes 90 days and B takes 30 days. So per day calculation (1/90+1/30) = 22.5 days.

Vinod Anand said: (May 22, 2013)
If A is thrice as good as workman B, Than A=3B ----(1) or B=A/3 --------(2). If A is finish a job in 60 days less than B. Than A = B-60. Put the value of B from Eq.(2). A = A/3 -60 3A = A-180 2A = 180 than A = 90 Days. Same Put the value of A in Eq.(2). B=90/3 = 30 Days. So Working together (A+B) = 1/90 + 1/30. A+B = 2/45. or A+B =45/2 = 22.5 or 22 1/2. Answer.22 1/2 Days.

PARASHAR said: (May 31, 2013)
Simple yaar. >A is thrice as good as workman as B and therefore is able to finish a job in 60 days=IF B TAKE 90 DAYS THEN A WILL TAKE 30 (60 DAYS LESS). >1/30 (PLUS) 1/60=4/90==>90/4==>22. 5 SIMPLE.

Thirupathi Malavath said: (Jul 24, 2013)
Simple method: Say B completes the work in 'x' days. Then A will take (x-60) days to finish the work. Since A is thrice as good as B, 3A=B. Therefore, 3 (x-60) =x, x=90. B's 1 day work=1/90, A's 1 day work=1/30. (A+B) 's 1 day work= (1/90+ 1/30) =2/45. Therefore, both can finish the work in 45/2 days i.e., 22 1/2.

Ankush Rana said: (Aug 9, 2013)
A is twice as good as workman B and together they finish a piece of work in 14 days. A alone can finish the work in.

Sam said: (Aug 10, 2013)
Did they mention that difference of working time is 60 days.

Shivaram Vollala said: (Aug 21, 2013)

In the given question the ration of capacity of work in day a:b is = 3:1. So always inverse proportion to capacity and work like the way a and b can do the work ration =1:3 i.e. a's one day work = b's three days work. So let now finish work together is imagine x. Ratios of each person a's work = x* 1/4 = X/4. (1). Ration of b's work = x* 3/4 = 3X/4. (2). In the given question difference is 60 days. So 3X/4-X/4 = 60 Days. Solove ther x we get x = 120. Now substitute x in (1) and (2). W e get a's part of one day work = 30 days. And b's part of one day work = 90 days. Now solve the. A and B together work = 1/30+1/90 = 4/90 =2/45.

This is and b together part of work now one day work = 45/2 = 22.5 days.

Sudhanshu said: (Sep 19, 2013)
Why so many stories I don't know. Its as simple as this: A's 1 day's work = x. B's 1 days work = x+60. So, total one day's work is. 1/x + 1/x+60 = 1. And you get x = 30 that is total days required for A to cmplete the work where B's value gets 90 days. Rest you can solve.

Malay Kanti Bhunia said: (Sep 21, 2013)
X - 3X = 60. X = 30. A done works 30 days and B done the work 90 days. A work done in 1 day 1/30 part. B work done in 1 day 1/90 part. A and B work together in 1 day (1/30+1/90) = 2/45 part. Time taken in this work 22.5 days.

Jag Parvesh said: (Dec 22, 2013)

Ratio of times taken by A and B to finish a work is 1 : 3. A:B=1:3 OR A/B=1/3 or 3A=1B --(1). B-A = 60. B-(1/3)B = 60 (Substituting the value of A from eq 1). 3B-B = 180 (Multiply through by 3). 2B = 180. B = 180/2. B = 90. A = (1/3)*90. A = 30. So, A can do the job in 30 days. Therefore, A can do 1/30 of the job per day. And B can do the job in 90 days. Therefore, B can do 1/90 of the job per day. Work they can do per day: = (1/30) + (1/90). = (3/90)+(1/90). = (3+1)/90. = 4/90.

So the job will take 90/4 days, which is 45/2 or 22.5 days.

M Ahmad said: (Feb 4, 2014)
A can do the job in x days. B can same job in 3x days. 3x=x+60 by B. x=30. One day work by A and B = 1/30+1/90 = 4/90 = 2/45. Whole job done by A and B = 45/2 = 22.5 days.

Michael said: (Mar 25, 2014)
How do we get 4/90 ?

Mancy said: (Apr 12, 2014)
Hi @Michael, By taking the L.C.M of 30 & 90 you'll get 90. Now, here the value become. =1/30+1/90. =(3+1)/90. =4/90. =2/45. So, 2/45 is total work done by them, But we've to find the days. By formula work to days. N work = 1/N days. So, 2/45 = 45/2 days. Answer = 22.5days.

Sundar said: (Apr 23, 2014)
Please Tell me how 3/2 has come?

Atul1487 said: (Apr 28, 2014)
What is need to take time difference? How will I come to know that I need to calculate time difference?

Venkatesh said: (May 21, 2014)
Hi friends just read, A's works 3 times than B so work ration 3:1 and time ratio will be 1:3 in the question they ask for time so 3/(3-1)*60=90. A 3 times better 3/90=1/30(1 days work) B 1/90 1days work together 1/90+1/30=answer.

Poornachandran said: (May 24, 2014)
Guys, I'll tell by simple method. Given, A is thrice of B. So A = 3B---->(1). A's 1 day work is A=1/60--->(2). Substitute (2) in (1), A=3B. We get, 3B=1/60. B=1/180. In question they asked A+B=how many working days? We know A and B values. Add A and B. 1/60+1/180=1/Work days. Take L.C.M. 3+1/180=1/Work days. 4/180=1/work days. 1/45=1/work days. Work days=45. By fraction we can write 22 1/2 days.

Kumar said: (May 26, 2014)
How its "4/90 " ?

Nithya said: (Jun 24, 2014)
Lets B takes x days to complete the Work, Then B 's Capacity ==>1/x. A is 3 times as good as A so A'S capacity is 3/x. Then Time Taken by B is = x/1. Time taken by A is = x/3. Time difference (x-x/3)=60. Which gives x = 90. Time taken By B = 90. Time taken By A = 30. (A's Work +B's Work) 1 day Work = (1/30)+(1/90). = 4/90. Then Time taken to complete work is 90/4 ==> 22.5 days.

Pranay said: (Jul 13, 2014)

The work being done by A & B is in ratio of 1:3. This means if A does a work in 1 day, than B will do this work in 3 days. Now let suppose this ratio is multiplied by a factor, say x. Then ratio becomes x:3x. Now another relation given is that A can do work 60 days faster then B. Mathematically we can write it as. x=3x-60. Solving this, we get x = 30. Hence the ratio becomes 30:60.

Now we can calculate the time taken by them.

Thaha said: (Jul 22, 2014)

"A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B." Solution: ********* 'A' able to finish a job in 60 days 'less than B'. Let A's work is = x days. Let B's work is = 3x days. A able to do a work in 60 less than B. Therefore, A's work = B's work - 60. So, x=3x-60. Then x=30. A can complete the work in 30 days. B can complete the work in 3*30 = 90 days. A's one day work = 1/30 days. B's one day work = 1/90 days. A+B one day work = (1/30)+(1/90) = 4/90 days. Therefore A and B can finish the work in = 90/4.

So the answer is : Option [B].

Kalyani said: (Jul 28, 2014)
What is the meaning of taking 3/2 in the problem. What's that ratio about?

Piyasa Dey said: (Aug 20, 2014)

If A does a work in 1 day. therefor B does the same work in 3 days since A is thrice as good as workman as B. Let A completes the work in x days, B will take (x + 60) days more than A takes. Therefore 1:3 :: x :(x + 60). Now according to the formula if a:b :: c:d. Then it is considered as (a * d) = (b*c). Applying this formula we get 1*(x + 60) = 3*x. By solving we get x= 30 i.e A takes 30 days to complete the work. Therefore B will take (30+60)=90 days. A's one day work = 1/30 days. B's one day work = 1/90 days. A+B one day work = (1/30)+(1/90) = 4/90 days.

Therefore A and B can finish the work in = 90/4.

Deepak Patgar said: (Aug 22, 2014)

Let A completes work in x days. So no of days taken by B to complete the same work will be 3x days. A takes 60 days less than B. So 3x-60 = x. 2x = 60. x = 30 days (number of days taken by A). 3x = 90 days (number of days taken by B). Work done by A per day is 1/30. Work done by B per day is 1/90. Work done the together in 1 day will be (1/30+1/90) = 4/90. So work done by them in 10 days will be 40/90. Work done in 20 days 80/90. Number of days require to do the remaining 10/90 will be 2.5 days.

Ans = 22.5 days.

Poor Gamer said: (Aug 29, 2014)
Let A takes x days and B takes 60+x days. Its given that A takes 1 days when B takes 3 days. So, 1/3 = x/x+60. Cross multiply and we get x = 30 i.e A. X+60 = 30 + 60 = 90 i.e B. Remaining as usual.

Divyanshu Dwivedi said: (Sep 2, 2014)

Simple: A's work = x. B's work = y = 3x. Hence acc. to ques.: 3x - x = 60 ;. x=30 A's. y=90 B's. Now.... 1/30 + 1/90 = 1/z.

z = 90/4 Answer.

Mohit Jain said: (Dec 4, 2014)
Let, A takes = x days. B will take = 3x days. Difference 3x-x = 60. So 2x = 60. x = 30 days. Thus A can do it in 30 days and B in 90 days.

Sumit said: (Dec 8, 2014)
If difference of time is 60 days, B takes 3/2 x 60 = 90 days. Please explain this statement.

Prakash said: (Dec 15, 2014)
But there is not given difference in question they given A finish work in 60 day?

Ankita said: (Jan 12, 2015)
If B takes y days , A takes (y-60 ) days. Now , their efficiency are A:B = 3x : x. So total unit of work is 3x(y- 60 ) man days = xy man days. Calculating this we get y = 90. So if B worked for 90 days, A worked for 30 days. Hence 1/30 + 1/90 = 22 1/2 days :).

Priya said: (Mar 17, 2015)
No need to do all that simply guess numbers 30 & 90 which is satisfying this then without using pen we can get answer 22.5 days.

Ankita said: (Apr 5, 2015)
Suppose A takes x days. Then, B will take 3x days. From question, 3x-x = 60. => x = 30. => A takes 30 days and B takes 90 days. Together they will take = 3090/30+90. = 3090/120. = 90/4. = 22.5 or 22 1/2 days (ans).

AaA said: (Apr 7, 2015)
Is there a fixed formula for this?

Govardhan Reddy said: (Apr 9, 2015)
Why were their difference between days? Please explain to me.

Sachin said: (Apr 28, 2015)
Its very simple. Suppose B's done work = X day. Then A's done work = (X-60) day. Efficiency ratio is. A : B = 1:3. (X-60) : (X) = 1:3. X = 90. So A's take days = 30. B's take day = 90. A's 1 day work = 1/30. B's 1 day work = 1/90. (A+B) s 1day work = 1/30 + 1/90 = 2/45. So together they will take = 45/2.

Raj said: (May 15, 2015)
Easy lets assume A works total days = X. So A one day work = 1/X. B is working 3 times less than A. So Total days of B is = 3X. So B Works one day = 1/3X. Different between total days of B and A is 60. So 3X-X = 60. 2X = 60. X = 30. Now normal maths. Replace X with numbers. You will get answer. So 1/30-1/90 = 22.5.

Arjun said: (May 18, 2015)
Can any one give me a easier way using LCM method?

Mohit Agnihotri said: (May 25, 2015)
Work done ratio (A:B) = 3:1. And let x be no. of days taken by B. So, A:B = x-60:x {Given- A finish a job in 60 days less than B}. Now, (x-60)/x = 1/3. 3x-180 = x => x = 90. It means A takes 30 days and B takes 90days. One day work of A and B is 1/30+1/90 = 4/90. Thus, 90/4 = 22.5 days required to complete the work.

Pratyush said: (Jun 8, 2015)
Can we do it like this: a = 3b....(1). a-b = 60. 3b-b = 60. 2b = 60. b = 30. If b = 30 then from 1a = 3x30 = 90. Now, = 1/30+1/90. = 3+1/90. = 4/90 = 2/45. = 45/2 = 22.5 days.

Neeraj said: (Jun 11, 2015)
Shortcut: A & B together will complete in 6/14/8 = 24/7 days = 3 3/7 days. Work completed in 3 days. So C's share 3/7 days. Now 3200/24/7*3/7 = 400.

Rajat Singh said: (Jun 16, 2015)
Simple solution: a = 3b. a-b = 60 (difference of b). 3b-b = 60. b = 30, a = 90. So they can together work in 1/30+1/90 = 4/90. :->22.50.

Megala said: (Jul 2, 2015)
Please explain last 2 steps.

Surya said: (Jul 11, 2015)
Simple formula with solution: (D) n/n2 (i.e n square)-1 = work together. Details: D-60, n-3, by putting the formula = (60)3/3's square-1 = 22.5 days.

Sharad said: (Jul 15, 2015)
Given A is thrice as good as B, Therefore 3:1. i.e 3x:x (ability to work). (Time taken is inverse of work). Time taken by A and B to complete work = x:3x. Difference A-B = 60. Therefore x-3x = 60. x = 60/2 = 30. Now x:3x = 30:3(30). = 30:90. (A+B) 's 1 day = (1/30)+(1/90). 1 day = 2/45 work. 45/2 day = 1 work. 22. 5 day = 1 work.

Malleswari said: (Jul 20, 2015)
A is thrice as good as B means 3A = B. A finish the work 60 days less than B means A = B-60. So, 3(B-60) = B. 3B-180=B. 2B=180. B=90. Then, 3A=B. 3A=90. A=30. So, A's I day work is 1/30. B one day work is 1/90. Then (A+B) 1 day work together is (1/30+1/90) = 2/45. Total days they work together is. 45/2 = 22.5.

Manju Gouda said: (Jul 21, 2015)
Let us take B's work days be 'x'. Then A's will be x/3. Given difference is 60. Therefore x-x/3 = 60 on solving x = 90. Therefore B days = 90 & A = 30. A&B together will be (90*30)/(90+30) = 22.5 days.

Lins said: (Jul 31, 2015)
1:3 = x:(x+60). 1/3 = x/(x+60). So x+60 = 3x. 60 = 2x. Then x = 30.

Satyawan said: (Aug 13, 2015)
The explanation given above is very difficult to understand please try to explain the concepts as simple as possible.

Naresh said: (Aug 14, 2015)
1:3. Total 4 parts. 90/4=22.5 (one part). Here one part means A's work. Remaining 77.5 belongs to B.

Ravi Yadav said: (Aug 23, 2015)
Let A takes x days and B takes y days to complete work. In one day A completed 1/x part of work and B 1/yth. According to question 1/x = 3*1/y and y-x = 60. By solving x=30 and y= 90. So in one day both completed (1/x + 1/y) = 4/90. They can do it in = 90/4 = 45/2.

Nil said: (Aug 25, 2015)
A 1x -- = --- (RATIO OF TIME) B 3x And difference is given 60 days. 3x-1x=60. 1x = 30 days for A. 3x = 90 days for B. I don't remember but I think I have posted the another method up above long time before.

Rahul said: (Aug 25, 2015)
Can we solve such questions by LCM method? Please help.

Ramesh said: (Sep 24, 2015)

Time ratio between A and B is 1:3. A/B = 1/3------ (1). B takes thrice the time taken by A. A-B = 60 from A = B+60--- (2). BY substituting (2) in (1). Then get time taken by B to finish work in 90 days. From (1) you get time taken by A to finish work in 30 days. A's 1 day work is = 1/30. B's 1 day work is = 1/90. (A+B) 1 day's work is = (1/30+1/90) = 2/45.

Then time taken by the A and B working together is 45/2.

Anshul said: (Oct 5, 2015)
We can solve this question easily. A:B = 1:3. Difference is 60. Hence ratio becomes: A:B = 30:90 = 1:3. Here we can see diff is 60. So our answer will be 90*30/90+30 = 270/12. = 90/4 = 45/2 = 22+1/2.

Salman said: (Nov 15, 2015)

So much confusing answer given. This is basically ratio problem. 60 days less means you have to take ratio of time and solve the problem. A is thrice as better as B means. B takes thrice time compared to A. i.e Ratio of time taken by A/B = 1/3. If B takes x days then A takes x-60 days time to complete the work. i.e Ratio of time taken by A/B = x-60/x. Therefore 1/3 = x-60/x. Solve to get x = 90 therefore B takes 90 days and A takes 30 days. Daily Work of A = 1/30. Daily Work of B = 1/90. Adding work of A and B. Daily work of A and B is 4/90. So time taken for both A and B to complete the work is 90/4 = 221/2 days!

Simple as that!

Nilu said: (Dec 8, 2015)

A is thrice good as B. So, ratio of work done is 3:1 and A taken 60 days less as compare to B. Let time taken by B is x so time taken by A is x-60. So 3:1::x:x-60. 3x-180 = x. So 2x = 180 and x = 90. Time taken by B = 90 days so time taken By A is 30 days. A's one day work = 1/30 and B's one day work is 1/90. Total work done by both A and B in one day = 1/30+1/90.

= 3+1/90 = 4/90 = 2/45 = 22.5 days.

Pratim Pal said: (Jan 6, 2016)

Hi friend. This is one of easiest problem. Here given that the ratio of time taken of A and B to complete one work in individually is 1:3. So let us take A can do this work in X days and that of B is 3X days. According to conditions B took 60 days more than A. 3X-X = 60. 2*X = 60. X = 30. So time taken by B is 3*30 = 90 days and by A is 30 days. When A&B together do this work. The required time is: = 1/(1/30+1/90). = 1/((3+1)/90).

= 45/2 days.

Sagar said: (Jan 7, 2016)
Please tell me how is the difference of time is 60 days?

Sudip Purakait said: (Jan 19, 2016)
Hi @Sagar. It is mentioned in the question.

Mukunda Saini said: (Jan 27, 2016)
A is thrice as good as B. So A = 3x and B = x. A is 60 greater than B. So 3x-x = 60. 2x = 60. x = 30. A = 90 and B = 30. 1/90+1/30 = 45/2. Answer: 22 1/2.

Sravan said: (Jan 30, 2016)

Since it's mentioned that A completed 60 days less than B. We have to know there less than rate. Since it given A is thrice as good as B. That means it takes 1 day to A to do Bs 3 day work. So now we can know that A can do in (3-1) = 2 days less than B. That means A less than days for B days for 2 its 3. Similarly for 60 less day we need to multiply 2 by 30 to get 60. Since we do on 2 (A) side we have to multiply on 3 (B) side then we get. = 2x30 : 3x30. We get = 60 (for A day's lesser than B) : 90 (we got B days) that means A work days = 90-60 = 30. So 1/30 + 1/90= 0.0444 amount of work per 1 day. For 1 piece of complete work 0.4444/0.4444 = 1/0.4444 days.

That 1 piece of work done for 22.5 days by A & B together.

Bhupinder said: (Feb 4, 2016)
Good explanations thanks.

Vamshidhar said: (Feb 5, 2016)
In the explanation, said that, "If difference of time is 60 days, B takes (3/260) = 90 days. My opinion is if A can complete work in 60 days then B should complete work in 360 = 180 days but not in 90 days. Can anyone explain this part?

Ram said: (Feb 15, 2016)
Guys, this is pretty simple. Given A : B = 3 : 1, difference in time taken is 2. Let us consider it as 2 parts. Then it's also given that A can complete the work with 60 days gap to B. Hence we can equate these 2 parts to 60 days. Therefore 2 parts = 60 days. A's part is 1 parts = 30 days. B's part is 3 parts = 90 days. Rest you know. Hope you intelligent guys understand :).

Bunny said: (Apr 1, 2016)
How to do LCM?

Dipa said: (Apr 1, 2016)
3x:1x => 3x - 1x = 60. => 2x = 60. => x = 30. => 3x = 90. A+b together work = 90 * 30 / 90 + 3. => 2700 / 120 = 22.5 days.

Pari said: (Apr 18, 2016)
Thanks for giving a different solution.

Guarav said: (Apr 19, 2016)
A is thrice as good as B i.e A:B = 3:1. The ratio will be same. Now let a number of days for B be x. Thus, for A it becomes (x - 60) Now equate 3/1 = x/(x-60)(ratio of days of B to the days of A). 3x - 180 = x. x = 180/3. x = 90. No of days by B is 90. Hence days of A will be 30.

Ramya said: (Jun 3, 2016)
Thank you @Siva. It's simple to learn.

Inzamamul Haq said: (Jun 4, 2016)

Workman. A : B. 3 : 1. Time taken; A : B. 1 : 3. A) if B finish work in 30 days then, A can finish it in 10 days. Now the difference in a day is 20. B) if B finish work in 60 days then, A can finish it in 20 days. Now the difference in a day is 40. C) if B finish work in 90 days then, A can finish it in 30 days. Now the difference in a day is 60. Given question. The difference is 60 days. Hence, condition c) satisfies. A 1-day work is 1/30. B 1-day work is 1/90. A + B 1 day work is 1/30 + 1/90 = 4/90.

Days to complete the work is 90/4 => 22 1/2.

Mahesh said: (Jul 14, 2016)
Let consider B can do work in n days. 1 days work of B = 1/n. So, A = n - 60. 1 day work of A =1/ (n - 60). As given A = 3b. 1/ (n - 60) = 3 * (1/n). n = 90. B can do work in 90 days. So A can do in 30 days. Both = (1/30) + (1/90). = 22 (1/2).

Insane said: (Jul 26, 2016)
Let A be X where as b = 3x. So, 3x - x = 60. x = 30. a = 30, b = 90. Together they can do the work in 22 (1/2) days.

Priya said: (Aug 1, 2016)
Please say me any shortcut methods to solve this problem.

Anonymous said: (Sep 24, 2016)

Hello friends, I just want to clear out something and that is according to the formula given. Here the answer is not correct. There has been a mistake and that is it is wrongly solved becomes as the question goes hereby, 1) A is thrice as good as B so the ratio would be like 3:1. But it has been mentioned as 1:3 which is wrong according to my perception.

So please make it correct or give the correct sort of explanation to prove me wrong.

SscASPIRANT said: (Oct 21, 2016)
Hi guys Here is a trick to solve it. If B = 1, A = 3, Therefore efficiency is A : B = 3 : 1. Now, 60 days less means the difference of their efficiency. 2 ---> 60 1 ---> 30 Now you got 30. A = 3 * 30 = 90, B = 1 * 30 = 30, LCM = 90. Which is total work and total days = total work/total efficiency. T.D = 90/4 = 45/2 = 22 (1/2)days.

Vaishnavi said: (Nov 8, 2016)
Thanks @Sheetal it is best trick.

Mohin Uddin Mizan said: (Nov 10, 2016)
Let B takes X days to the work. Then B's 1 day's work = 1/x and A's 1/3x. ACQ, 1/x - 1/3x = 60, So, x = 1/90. As the difference is 60, so A needed 90 - 60 = 30 days. (A + B)'s 1 day's work = 1/90 + 1/30 = 2/45. So, to do the total work they need 45/2 or 22(1/2).

Soniya said: (Dec 17, 2016)

Let t1 &t2 are time taken by A and B. w1 & w2 are work done by A and B. Ratio of the time taken by A and B =1 : 3. Then, A = x, B = 3x (x is some constant). We know that t1 = t2 - 60 (A takes 60 days less than B). t2 - t1 = 60 3x - x = 60 (t1 = x, t2 = 3x) x = 30. Then t1=30 and t2 = 90. Total work done by A& B(W) = w1 + w2. W =1/t1 + 1/t2. = 1/30 + 1/90 = 2/45.

Then time taken by A&B to finish the work is 45/2days.

Dineshkumar said: (Dec 28, 2016)
Your answer is clear @Sundar, Thanks.

Udhay said: (Dec 28, 2016)
I can't understand it. Please someone help me.

Devendra Kumar said: (Dec 28, 2016)
Please tell me the easiest solution of this problem. Like LCM method.

Hari said: (Dec 30, 2016)
A:B = 3:1 efficiency. Because, A is Thrice the work as B. So, A complete the work 60 days before. Then 2---60 1--30, So to find total work we just take it as; A = 3 * 30. B = 1 * 30. Total work is 90(LCM IS 90). So, W = ED, D = 90/4 = 22.5.

BLACK said: (Jan 1, 2017)
Ratio of time taken by A & B = 1 : 3. Suppose B takes x days to finish the job. Then A takes (x-60) days. So, (x-60) : x = 1:3 x= 90. So rest are same.

@verma Ji said: (Jan 31, 2017)
Hello Friends: this shortcut formula is better to solve these type question in less time. Alternate Method: Since 'A' is 'm' times as efficient as 'B' & takes 'D' days less than 'B', then the time required to complete the job together is given by, T = m * D/(m^2 " 1) T = 3 * 60 / [(3)^2 - 1] = 180 / 8 = 22 1/2 days.

Hari. said: (Mar 17, 2017)
Thanks @Sachin.

Suresh said: (Mar 17, 2017)
A is 3 times more efficient than B, A=3B A do the work less than 60 days compared to B, A-60=B. So, we can write it as, A = 3(A+60) A = 3A+180 2A = 180 A = 90 90-60 = B B = 30.

JPV said: (Mar 21, 2017)
Ratio of no days taken to do work by and b= x : 3x. It's give that diff= 60. ie 3x-x = 60, ie x = 30. No of days taken by B=90. No of days taken by A=30. ie total no of days taken when work is done together= 1/30 +1/60, = 22 1/2.

JAY said: (Mar 21, 2017)
LET: A = 3B. where: A = 1/x and B = 1/(x+60) so; (1/x) = 3[ 1/(x+60) ] X = 30. 1/A + 1/B = 1/T 1/30 + 1/(30+60) = 1/T Then, T = 22.5 answer.

Sahil Husain said: (Mar 31, 2017)
A=3B ----------(1) A-60=B----------(2) from equation 1 & 2 3B-60 = B B=30 and A = 90 (A+B)'S 1 day work =1\90+1\30 = 2\45, So (A+B)'s work = 45\2 = 22 1\2.

Dipak said: (Apr 4, 2017)
Guys. I'm giving simple approach. 3x - x = 60 x = 30 So respective days are 90 and 30. Total days together = 30 * 90/120 = 22.5.

Dhruv said: (Apr 13, 2017)
Hi, According to me, the solution is; A= 3B + 60, So , A + B = 0 3B + 60 + B = 0 B = -15. How to get the correct answer? Please, anyone explain me.

Sambhav said: (May 4, 2017)
Hi guys. It is given that A is thrice efficient then B then the efficiency of A is 3x and that of Y is x. then no of days are For A is(60-y) and for B is y. Then total work done is constant then 3x(60-y) = x y. Then y = 45. Then total work done by A is 45 X. And rate of work of A and B will be 3x and x and if they work together the rate will be 4X. So no of days will be = 45/4.

Sasikumar said: (May 19, 2017)
Thanks @Deepti.

Esrak Ahmed Kafi said: (May 30, 2017)
Let B can do it in 3x days. So, A can do it in X days. According to Question, 3x-x = 60. So, X = 30. So, A can do it 30 days while B can do it in 90 days. Now in (1/30+1/90) days A & B can together do the work. =45/2 = 22.5 days.

Rakesh said: (Jun 13, 2017)
How 3/2? Explain.

Sumanth said: (Jun 21, 2017)
Thanks for your explanation @Indhu.

Nagesh said: (Aug 17, 2017)
Thank you for all the given explanation.

Pramod Patel said: (Aug 29, 2017)
I think the best and universal approach is this: A can do the work in X days, B takes X+60 days for same work, But (X+60)/X=3/1 as time taken by A and B is in 1:3 ratio, Solving we get X=30, A's one day work is 1/30, B's one day work is 1/90, combining their one day work we get 1/30+1/90=2/45, total time taken by them is 45/2.

Haritha said: (Aug 31, 2017)
It's a clear explanation. Thank you @Sheetal.

Tiya said: (Sep 19, 2017)
Please solve this question. If the ratio of work efficiency of A and B is 3:2. If A and B together finish a work in 5 days in how much days B alone complete the work?

Bismi Maria Jose said: (Sep 22, 2017)

It is said A is 3 time as good as B. ie. A=3*B Again given, A is able to finish a job in 60 days less than B. say, B takes x days to complete 1 work therefore A takes x-60 days to complete 1 work(same work) A's 1 day work=1/x-60 B's 1 day work=1/x. Substituting; Applying in formula, A=3B ie. 1/x-60=3/x so,x=90 x-60=30 so we got the number of days A alone and B alone worked i.e 60 and 90 1 day work of (A+B)=1 / 60 + 1 / 90 = 2/45, So,nobr of days (A+B) worked = 45/2,

Answer is option B.

Purusottam said: (Sep 27, 2017)
The answer must be 45 days. Let B does the work in x days. Now let's think about A's efficiency. As far as the question is concerned, 3100/x =100/60. So, x=180, Efficiency of A+B=100/60+100/180, = 20/9%. So 20/9...........1 1..............9/20 100..........9/20100 . =45.

Purusottam said: (Sep 27, 2017)
Yes, correct @Sugumaran.

Anupam Kumar said: (Oct 1, 2017)

Let us understand this in a much simpler way. Let the time taken by B to finish the work be X days. Then according to the question Time is taken by the A is (X-60). Work done by B in one day is (1/X), Work done by A in one day is (1/X-60), And we know that A is three times faster than B, So work done by A in one day is three times the work done by B in one day. So 3*(1/X)=(1/X-60), 3X-180=X, X=90, Therefore B takes 90 days to complete the work hence A take 30 days to complete the work, therefore together they take 1/(1/30+1/90) days, which is equal to 45/2.

Thank you all.

Saikrishna said: (Oct 22, 2017)
a b x 3x 2x=60 so x=30 total work=3*30=90 Ans=90/4=22 1/2.

Rohi said: (Oct 26, 2017)
Ratio of times taken by A and B = 1:3. Means B will take 3 times which A will do in 1 time. If difference of time is 2 days, B takes 3 days, If the difference of time is 10 days, B takes (3/2) * 10 =15 days.

Biplab Sarkar said: (Oct 30, 2017)
Here given k=3, n=60. So formula is -> kn/ (k^2-1) =3*60/ (3^2-1) =180/8=22 1/2 days.

Shaman said: (Oct 30, 2017)
Please provide the solution of if A is 5 times better than B together they complete the work in 50 min then B alone can do the work in how many minutes.

Jack said: (Oct 31, 2017)
Can anyone explain me why the step 3/2*60 used. I couldn't get the logic of finding difference as 2.

Pramod Nepal said: (Nov 6, 2017)
Let see @Shaman. A finish work in x day and B can 5x day. Then we can do A+B= 1/x +1/5x. We have A+B = 50, 50 = 5x/6 after sol x= 60 it means A can do in 60 min and B 300 min.

Nik said: (Nov 8, 2017)
How 4/90 comes?

Rizwan said: (Dec 19, 2017)
From where does this 4/90 comes? How 4?

Vishal said: (Dec 27, 2017)
I have better solution. A:B-3:1(rate). A:B-1:3(days). Diff of 2 between ratio of days which is equivalent to 60 and 230=60. Hence 30 will be multiplied to 1 and 3. And we get 30 and 90. Together days taken= 30 90/30 + 90 = 22 1/2.

Dusu Opo said: (Jan 17, 2018)
Why 60 days? Please explain.

Sherin said: (Jan 18, 2018)
Thank you @Showry.

Jiban said: (Feb 10, 2018)
Can it be in this way? B will take 180 days more than A. Then calculate for 1 day. Can anyone solve this?

Nurun Nobi Khokon said: (Jun 1, 2018)
Let A take x days So, B takes x+60 days 3x = x+60 (B took 3 times more, so to make the equation equal he have to multiply the days taken by A by 3). or, 2x = 60, or, x = 30 days. A takes 30 days and b takes 30+60 or 90 days., Now, (A+B)'s 1 day's work = (1/30+1/90) or 4/90 or 2/45, So, total days required to do the whole work, 45/2 or 22.5 days.

Kavitalodhi said: (Jun 7, 2018)
In the question clearly, say that A takes 60 days less than B. So A can do the work in B-60 days, And time ratio of A:B = 1:3, 1/3=B-x/B =>B=90,A=30. So, A and B can do the work together 1/30+1/90 =>2/45, Mix fraction of 2/45 is 22 1/2.

Mohit said: (Jun 15, 2018)
3 x 60/3^2-1 = 22 1/2.

Balaji said: (Jun 28, 2018)
Capacities of A:B=3:1. Time taken ratio of A:B=1:3. Difference of ratio in time is 2 = 60 days => A takes 30 days and B takes 90 days => 90/4=22 1/2.

Balaji said: (Jun 28, 2018)
Capacities of A:B=3:1. Time taken ratio of A:B=1:3. Difference of ratio in time is 2 = 60 days => A takes 30 days and B takes 90 days => 90/4=22 1/2.

Balaji said: (Jun 28, 2018)
Capacities of A:B=3:1. Time taken ratio of A:B=1:3. Difference of ratio in time is 2 = 60 days => A takes 30 days and B takes 90 days => 90/4=22 1/2.

Balaji said: (Jun 28, 2018)
Capacities of A:B=3:1. Time taken ratio of A:B=1:3. Difference of ratio in time is 2 = 60 days => A takes 30 days and B takes 90 days => 90/4=22 1/2.

Rajashekar said: (Aug 9, 2018)
Shortcut of these type of problems: A&B = Difference * 'n' times / n^2 - 1. = 60*3/3^2-1 = 180/9-1. = 180/8=22.5 or 22 1/2.

VICKMA said: (Aug 11, 2018)

Here A is thrice EFFICIENT than B. A=1 B= 3 A takes 60days less than B to finish a work, This shows that if B takes to complete a work by "X" days. Then A will take X - 60 days to complete a piece of work. We know that A=1. B=3 A= X - 60 B= X (No.of day to complete a work). Cross multiply: 3(X-60)=X => 3X-180=X, -180=-2X => X= 90. WORKING TOGETHER: A+B = 1/X-60 + 1/X. We know that X = 90, A+B = 1/90-60 + 1/90, =1/30+1/90, =(3+1)/90 => 4/90 => 2/ 45. Therefore, A+B takes 45/2 days to complete a piece of work.

A+B = 22 1/2.

SWETHA said: (Aug 25, 2018)
Since A finishes the job in 60 days less, from (ii) we get: 3X - X = 60. A=30 B=90, A+B=1/30+1/90. =2/45. A and B together can do the work in 45/2=22 1/2.

Naidu said: (Sep 5, 2018)
It is a good and clear method, Thanks @Prashant.

OM PRAKASH REDDY said: (Sep 27, 2018)

NO RATIO'S. A is thrice as good as B. This implies that if B take '' T '' days to complete the work, then A takes just ''T/3" days for same amount of the work. Now coming to the second point in the question, A takes 60 days less than what B takes. T/3 = T - 60. ----> T=90, ao B takes 90 days alone which implies A takes 30 days alone to complete work.

If A and B work together then no.of days required would be (1 / (1/30)+(1/90) ) which results in 22.5days.

Parveez said: (Sep 27, 2018)

A is thrice as good as workman as B so the ratio of time taken by A and B is = 1:3. Let, A completed the work in x days. B completed the work in 3x days. A's 1-day work= 1/x and B's 1-day work= 1/3x, So, A+B 's 1-day work= 1/x+1/3x, =4/3x. So, A+B completed the work in 3x/4 days. Since, A finishes a job in 60 days less than B. therefore , 3x-x=60. x=30. therefore, Working together A+B completed the work in 3x/4 days. = 3*30/4. = 45/2.

= 22 1/2 days.

Shreya said: (Nov 13, 2018)
@All. This is the easiest & shortest!. Let a be x whereas b = 3x. So, 3x " x = 60. x = 30. therefore a = 30, b = 90. so when they work together-> 1/30+1/60 = 4/90 = 2/45. Together they can do the work in 22 (1/2) days.

Swarani said: (Dec 16, 2018)
Your explanation is easy, thanks @Showry.

Jeev said: (Mar 1, 2019)
3A = B. If 60 is less than b(then 60 is two times of a) then A=30, b = 3 * 30 = 90, a+b=1/30+1/90, 3*1/90+1/90, (3+1)/90. Where 4/90(to get days upside down). 90/4 = 22(1/2) days.

Chacha said: (Mar 3, 2019)
It's simply. 3a = b.

Manohar said: (Mar 20, 2019)
A+B = 1/60 + 1/180. A is three times more efficient than B. (So that if a takes 60 days then B takes 180 days). And therefore; 2(A+B) = 180/4 = 22 * 1/2.

Chawdharya said: (Mar 26, 2019)
A : B TIME 1/3 : 1. DAYS X-60 : X. X-60/X = 1/3, X= 90, X-60 = 30. A work efficiency = 1/90, B work efficiency = 1/30, A+B work efficiency = 1/90+1/30, = 2/45, work efficiency = work/time. work is constant,so time = 45/2. = 22.5.

Ameer said: (Apr 1, 2019)
Thank you, excellent explanation. a = 3b --> (1). a-b = 60. 3b-b = 60. 2b = 60. b = 30. If b = 30 then from 1a = 3 x 30 = 90. Now, = 1/30+1/90. = 3+1/90. = 4/90 = 2/45. = 45/2 = 22.5 days.

SAMANTH KUMAR said: (Apr 11, 2019)
Let A=X ,B=X+60 (GIVEN A TAKES 60 DAYS LESS THAN B,I CONSIDERED B TAKES 60 MORE DAYS THAN A). Now, LCM OF X,(X+60) = X(X+60), Efficiency of A=(X(X+60)) / X = X+60, Efficiency of B=(X*(X+60)) / (X+60) = X. Total work of A&B = (X(X+60))/(X+X+60), We have A=3B (GIVEN). X = 3(X+60), X = 30. Put in the equation and get the answer 45/2 =22(1/2).

Priya said: (May 16, 2019)
The solution is; A = x , B = 3x x = 3x-60 x = 30 A = 30; B = 90; 1/30 + 1/90 = 2/45 = 22.5 days.

Harsh said: (May 25, 2019)
I am not understanding anything this, please explain.

Anitha said: (Jun 8, 2019)
A:B = 1:3 2p = 60 P = 30 30 : 90 1/30 + 1/90 = 2/45 = 22.5.

Sai said: (Jun 23, 2019)

A is thrice as B, A:B=1:3. B takes 60 days more than A to complete the work. Lets consider A to complete the work in x days, therefore, B completes the same work in (x+60) days, x:(x+60). Therefore, As these are equally related to one and other; 1:3::x:(x+60). Cross multiply we get x=30 days ie A can finish the work in 30 days, Therefore B can do it in 90 days ie 3 times more days given. Therefore: (1÷30)+(1÷90).

= 22.5 days.

Tachime Sangma said: (Jul 4, 2019)
How come 4/90? I don't understand.

Meg said: (Jul 21, 2019)

First thing, the work done is always same, i.e. Work done by A = work done by B = work done by A+B. So, if A does a work in x days then B does it in 60-x days. Now, we can write A=3B So, work done by A will be = 1*x = x Work done by B will be = 3*(60-x) As we know work done remains same then x = (60-x)*3. x = 45, So, A's total time = 45. B's total time = 60-x = 60-45 = 15. So, now we can find the total time taken by A+B to complete the work as, 1/15 + 1/45 = 4/45. It's one day work of A+B so reciprocal it to get the total time taken by them.

45/4 = 22.5 days

Subhendu said: (Aug 22, 2019)
(3-1)=2------>60 1------>30 3------->90. 1's day work for A= 1/30 1's day work for b=1/90 Both 1's day work=(1/30+1/90) = 4/90. Total day = 90/4. = 22(1/2). The answer is B.

Neena said: (Aug 25, 2019)
We can simplify it. Assume if B worked for 90 days and C worked for 30 days. B's 1-day work = 1/90. A's 1-day work = 1/30. A+B = 4/90 work. ie, 90/4 = 22.5.

Yash said: (Sep 23, 2019)
(TT.D)/(T^2-1). T-EFFICIENCY. T.D-TIME DIFFERENCE. So; 360/9-1 = 22.5.

Yaswanth said: (Sep 23, 2019)
Let's assume A completes its work in x days. B completes in 3x days . since A is times efficient than B. now, their difference is 60 days. then, x-3x=60, 2x=60, x=30, A=30,B=90. So, one days work of A and B together is A+B=1/30+1/90. =4/90, =2/45, So one day work of A and B together is 2/45. So A and B can complete the work in 45/2 days. this equals to 22(1/2).

Sanishk said: (Oct 15, 2019)
What is wrong with the below step? A's 1-day work = 1/y. Then, B's 1-day work = 1/3y. Now, A completes work before 60 days compared to B. So, 1/y - 1/3y = 1/60 2/3y = 1/60 y = 40. i.e., A completes in 40 days and B completes in 120 days, Now, working together they complete in 1/A + 1/B = 1/40+ 1/120 = 1/30. So, Together they complete in 30 days.

Rohan said: (Oct 16, 2019)
A and B Work 3:1 Time 1:3 i.e. 30:90 ......multiply by 30. And also they have given that the difference between the time taken to complete the work is 60. Hence when A and B time to work together, 1/30+ 1/90 = 2/45, Defer for A and B to complete the entire work they require 45/2 which is equivalent to 22 and A half-day.

Aravind said: (Nov 19, 2019)

Hi, friends, it's a bit tricky. First, they found the time difference to do work between a and b. Because the data we have is time difference in qn for 60 days consider. Then. If a takes 1 day. B takes 3 days. So. For 2 days time difference : 3 days for b Then multiply both sides by 30 since the time difference is given For 60 days time difference: 90 days of b. I hope you all get it.

Then use ratio. A takes 30 days to complete work.

Dinesh said: (Dec 3, 2019)
Please tell how A is working 30 days. How we calculate I don't understand.

Priti said: (Dec 11, 2019)
*shortcut method**** D= no of days. n= n times as fast. Dn/n^2-1 603/3^2-1 180/9-1 180/8=90/4=22 1/2.

Abhijith said: (Dec 24, 2019)
Can someone provide a solution for this problem using percentages or the efficiency ration ?

MOSA said: (Jan 20, 2020)
Let a did this work in X days. B can do it in 3x days. X+60=3x. X=30. It means A can complete this work in 30 days and B in 90 days; Capacity of; A is 3. B is 4. A+B= 4. TIME =90/4.

Rajesh said: (Apr 1, 2020)
Work=3:1. Time 1:3. 2 part=60 (difference). 1 part=30. 130:330=30:90. He asked work of B( 90)can do by both in how many days. 90/(1+3)= 90/4=22.5 days.

Naga said: (Jun 30, 2020)

The ratio of work done by A & B= 1:3. (Because A is thrice as good as B) A' s work done = Less than 60 days than B. So take B's work done = x days---(1) Then A's work done = x-60---(2) So, 1=x-60, 3= x. So cross mutiply as per the ratio simplification. x * 1= 3(x-60), x=3x-180, 3x-x=180, x =90. As per (1) & (2) B's work done = 90 days, A's work done = 90-60 = 30 days, (A+B)'s 1 day work done = 1/30 +1/90=4/90=2/45,

Total work done = 45/2= 22 1/2 days.

Bindu said: (Jul 13, 2020)
3/2 *60, how come 3/2?

Billal Hossain said: (Jul 14, 2020)
x : 3x. 3x - x = 60, => 2x = 60, => x = 30, 1/30 + 1/90, = 4/90. = 22 (1/2).

Nirmala Rai said: (Jul 19, 2020)
Ratio of A:B=1:3(efficiency). =3:1(time will be opposite of efficiency). Time difference between A:B=2. 2 denotes =60, 1 denotes=60/2=30 A, 3 denotes =60/2*3=90 B calculate L. C. M of A &B = 90, A+B=90/4= 22(1/2)-Ans.

Rajeesh Kumar said: (Aug 7, 2020)
@All. We can easily convert it to a linear equation. Let B requires x days and forA it is y it is given,x = 3y. In the same way; X-60=Y By solving we have 2x- 180=0 :.x=90. and y=90 - 60 = 30.

Saurabh said: (Aug 12, 2020)
time diffence = 60days. A is 3 times better then b. That means A will do 3 times of work in day and B will do 1 time of A's work in 1 day difference = 2 times. Day difference = 60 1 time difference = 60/2 = 30. A will do the work in 30 days. B will do a work in 3*30 = 90days.

Atharv Pathak said: (Aug 19, 2020)
W1/w2 = d2/d1. W1 = 3w2. And d1 = d2-60. So, 3w2/w2 = d2/d2-60, d2 = 90, d1 = d2 - 60 = 90 - 60 = 30. 1/90 + 1/30 = 1/22.5. Ans 22 * 1/2.

Sagar said: (Aug 20, 2020)
Thank you for very simple answer @Malleswari.

Akshay Salekar said: (Aug 21, 2020)

Hi, friends. We know that A capability to do work is 3 times of B,ok Then the the ratio of Efficiency is A:B=3:1 And the ratio of time (days) is A:B=1:3 ...(The ratio get reverse because Efficiency and time are inversely proportional) Now, Time taken by A to complete work = (X) day & Time taken by B to complete work = (X+60) day. *We compare the ratio of time (X/X+60)=(1/3) get X = 30 ----> (1). From (1) we get A need 30 Days and B need 90 days Now take lcm of (A day and B-day). That is LCM of (30 & 90). A & B need to complete 90 work. So, the efficiency of A is (3 w/d) & B's efficiency (1w/d). When they together (A+B) = work done is (4w/d).

So (90w/(4w/d)) = 22 1/2.

Omkar Raut said: (Sep 1, 2020)
A:B = 1 : 3. Let's say A's work is x, then x : 3x. Now, 3x - x = 60. Given in question. 2x = 60, x = 30 Now,A = 30, B = 90.

Nidhu said: (Sep 12, 2020)
So, let's take the ratio as 3:1. Consider b - 60 = a. 3a - 60 = a, A = 30, 30 = b-60, B = 90. A + b = 1/30 + 1/90. = 2/45. Which is 45/2=22.5=22 1/2.

Bhairus said: (Oct 22, 2020)
A = 3B; A time : x-60; B time =x; In 1 day together work =1/(x-60) +1/x. And we also know (x-60)/x = 1/3; From this two got x = 90 and time from eq 1 is 22.5.

Dnyaneshwar said: (Nov 28, 2020)
A = 3B Suppose workdone in 1 day by 'B'= 1/n. Suppose workdone in 1 day by 'A'= 1/(n-60). We get eqn; 1/(n-60) = 3(1/n). So, n =90 days (Time taken by B to complete the work). A= 30 days. A+B = (1/30)+(1/90) = 22.5.

Sanky said: (Dec 6, 2020)
A:B = 1:3. B = 3A. Difference is 60days, therefore B - A = 60, 3A - A = 60, 2A = 60, A = 30 & thus B = 90. Now, 1/30 + 1/90 = 22.5.

Ranjana Shree said: (Mar 9, 2021)
We can simplify it. Assume if B worked for 90 days and; C worked for 30 days. B's 1-day work = 1/90. A's 1-day work = 1/30. A + B = 4/90 work. ie, 90/4 = 22.5.

Paru said: (Apr 8, 2021)
@Harsha You gave a very good explanation, thank you.

Ahamed said: (Apr 10, 2021)
Thank you all for explaining.

Apsar Khan said: (Apr 28, 2021)
If A completes the work in x days, B will do the same in 3x days. 3x - x = 60. 2x = 60. Then x = 30 and 3x = 90. (A + B) 's 1 day's work. =1/30 + 1/90. = 4/90. So, A and B together will do the work in; = 90/4. =>22 and 1/2.

Adheer said: (Jun 2, 2021)

If B completes the work in X days, then A completes the work in X-60 days. A is thrice good as workman as B then, the ratio of the time taken to finish the same work is 1:3 Then, (X-60) : X :: 1 : 3 Solving this, X = 90 Means B finish the work in 90 days and A finishes the work in 30 Days, Working together, their 1-day work, 1/90 + 1/30 = 4/90 = 2/45.

Mean working together, they finish the work in 45/2 = 22(1/2) days.

HMJ said: (Aug 14, 2021)

A=3B, A can finish the job 60 days less then B, Say, work=60. Capacity of B = (60/x) ----> 1 Cap of A = (60/x-60) ----> 2. As per the condition A=3B. Compare the above equation by putting the Capacity of A = 3 times Capacity of B. You will get x=90. Now put this x in above equations 1 and 2. You will get the cap of A = 2 and Cap of B = 0.66. Working together, Days= Work/(cap of A + cap of B). = 60/2.66,

= 22.5.

Astik Mandal said: (Aug 20, 2021)
A - 30d. B - 90d. lcm - 90(total work). Efficiency of A - 3. Efficiency of B - 1. Total Efficiency = 4 total. work/totalEfficiency=90/4=22.5.

Srikanth said: (Sep 9, 2021)
Thanks @Sundhar.

Padma said: (Oct 6, 2021)
Here a simple calculation is; A takes 1 part and B takes 3 parts. \ So A:B ratio is 1:3. total 4p.and the difference is 2,they did work in 60 days so 60p. 4p=60. p=15/1. B total working days 15*3=45. W/t is 45/2.

Sachin said: (Oct 10, 2021)
Thanks everyone.

Jeeva said: (Dec 17, 2021)
a ------ b x ------ 3x. 1/3 of the work is remaining = 1 - 1/3. = 2/3. 2/3 of the work is completed by b = 60 days. one of the work is completed by b = 60 * 3/2. b = 90. B one day work = 1/90. A one-day work = 1/30. a+b = 1/30 + 1/90. a+b = 4/90 a+b = 2/45. A and B together can do the work = 45/2.

Muhammad said: (Dec 22, 2021)
Let A's total work completion time be = n. B's total work completion time = 3n, Difference between B and A's daily work = 60. 3n - n = 60, 2n = 60. n = 30. Total daily work. =1/3n + 1/n, =1/90 + 1/30, =2/45, So total time to complete for both = 45/2 = 22.5.

HARINI said: (Mar 26, 2022)
Given; A = 3B; A = B - 60. Substitute A = 3B in 2nd equation(a=b-60). 3B = B-60 B = 30. Therefore; A = 3B = 90. A+B = (1/30 + 1/90) = 2/45. So, the answer is 22(1/2).