Is the age of a father is reduced by 5 and becomes double the age of the son who is one by fourth the age of his grandfather who is 60 years old find the age of the father?

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Discussion :: Problems on Ages - General Questions (Q.No.8)

The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:

[A].	12 years
[B].	14 years
[C].	18 years
[D].	20 years

Answer: Option D

Explanation:

Let the present ages of son and father be x and (60 -x) years respectively.

Then, (60 - x) - 6 = 5(x - 6)

54 - x = 5x - 30

6x = 84

x = 14.

Son's age after 6 years = (x+ 6) = 20 years..

Amit said: (Aug 17, 2010)
We can also solve this as below: Let six years ago son's age be x, and fathers age be 5x. Then sum of their present age (x+6)+(5x+6)=60 x+5x+12=60 6x+12=60 6x=60-12 6x=48 x=8 Hence six years ago son's age was 8 years and present age is 8+6=14 years Answer=after six years his age will be 14+6=20 years.

Sowmya said: (Sep 28, 2010)
Thanks Amit.

Vijay said: (Oct 13, 2010)
Thank you so nice and easy.

Shabana said: (Oct 30, 2010)
We can also solve as.. x = son age y = father's age x+y=60 -----(1) (y-6)=5(x-6)-----(2) by solving (1)&(2) we get x=14 ,y=46 after 6 yrs son age = x+6 = 14+6=20

Shoeb said: (Dec 14, 2010)
Thank for making this sum so simple....

Santosh said: (Dec 21, 2010)
Hey amit you already added 6 initially, (x+6)+(5x+6)=60 x+5x+12=60 6x+12=60 6x=60-12 6x=48 x=8 and at end we haveto add another 6 means 8+6=14 years ....then how it would be 20 so actual answer is also wrong

Parthi said: (Feb 11, 2011)
Thank guys.

Sirisha said: (Feb 28, 2011)
@santosh Amit is right. He taking as ago, present, after.

Pankaj said: (Apr 30, 2011)
Superb shabana keep it up.

Mrs Pallavi said: (May 19, 2011)
Son's age= x, father's age is y. x+y=60.........................(1) as per 2nd statement (y-6)=5(x-6) 5x-y=24........................(2) therefore solving equ. 1 & 2 x=14 & y=46 3rd condition Son age after 6 year 14+6= 20 year.

Jagadeesh said: (Aug 26, 2011)
Thanks pallavi.

Rajinder said: (Sep 9, 2011)
The sum of son and father's age can be written as S+F=60 ----------(1) before 6 years ago 5(S-6)=F-6 5S-30=F-6 5S-F=-6+30 5S-F=24 ----------(2) ADDING (1) and (2),weget 6S=84 S=84/6=14 put s=14 in ist weget F=46 Hence after 6 years Son;s age will be 14+6=20 years.

Priya said: (Sep 27, 2011)
Let s be son and f be father. s+f=60 this was 6 years ago there fore (s+f)-6=60-6 . . .here f=5s therfore substut s+5s-6=54 . . .6s=60 therefor s=10 aftr 6 years s=16 Please tell wats wrong with my logic.

Manoj Verma said: (Dec 1, 2011)
Suppose son's age=x father's age=y x+y=60 y-6=5(x-6) 60-x-6=5x-30 6x=84 x=14 after 6 years son's age=20

Appatakar said: (Dec 13, 2011)
Awesome pallavi thanks.

Yakesh said: (Feb 15, 2012)
Before(6 years back): 5x, x Present:5x+6, x+6 After 6 years:5x+12,x+12 and 5x+6+x+6=60 x=8 after 6 years = x+12 = 8+12 = 20.

Venkatesh said: (Feb 29, 2012)
A+B=60,--->1 6 yrs ago , (A-6)=(B-6)*5[bcz Six years ago, father's age was five times the age of the son] A-6=5B-30, A=5B-24, ----->2 By simplifying 1 and 2 we will get B=16. Aft 6 yrs B+6=20.

Selvi.K said: (Apr 19, 2012)
We will solve this problem by solving the two equation Consider son's age=Y, Fathers age=X. Let X+Y=60. (1) 6 years ago means Son's age=X-6, Fathers age=Y-6. So the equations changed as per the condition 5Y-6=X-6. We get, X-5Y=-24. (2). Solve (1) , (2). We get y=14, x=46. After 6 years the son's age=14+6=20.

Kauthik said: (Aug 6, 2012)
Father's age = x ; son's age = y x+y = 60; x-6 = 5y; y+6 = ? x = 5y+6 5y+6+y = 60 6y = 54 y = 9 Hence present age of son = y+6= 15. I got answer like this. what's wrong in this method.

Chandana said: (Aug 20, 2012)
I think so... it's after 6 years, in eqn x-6=5y u didnt reduced son's age to 6years(after 6years) x-6=5(y-6) then u get the answer.. x-6=5y-30 x=5y-24; 5y-24+y=60 6y=84 y=14 hence present age of son=y+6=20

Pandi said: (Aug 28, 2012)
Now son age x and father age is y then x+y=60---->1 six years before son=x-6, father=5(x-6) so y-6=5(x-6) y-6=5x-30 5x-y=24--->2 solve 1 and get x=14 x is present age after six years x+6=20

Rohan Magar said: (Aug 31, 2012)
@Amit thanks yar. Your method is easy and simple to understand :).

Muhammad Umair Kabir said: (Sep 20, 2012)
Let 'F' be the Father's Age and 'S' be the Son's Age. According to situation: F+S = 60 EQ ---- 1 F-6 = 5(S-6) , Which is F-6 = 5S-30 EQ ---- 2 F = 5S -24 EQ ---- 3 Put this in EQ 1 5S - 24 + S = 60 6S = 84 S = 14 After 6 Years Sons age will be S = 14 + 6 = 20

said: (Oct 15, 2012)
s=x f=y x+y=60......................(1) 6 years ago (y-6)=5(x-6) i.e y-6=5x-30 Therefore at present age we have y-6+6=5x-30+6 i.e y=5x-24 From (1) x+5x-24=60 6x=84 x=14 Therefore after 6 yrs sons age will be 14+6=20

Vijay Anand said: (Aug 23, 2013)
@Priya. Your logic is correct but you have to subtract 12 from 60. You have subtracted 6 for sons age and for fathers age you have to subtract another 6 know so it will be 60-12 = 48 not 54. If you want me to explain precisely means please let me know.

Sunil said: (Mar 30, 2014)
Fathers age 4 times of his son means. Sons age X. Fathers age 4x. Or Sons age 4x. Fathers age x. Which one is right ? How to solve explain ?

Nandhini said: (Apr 4, 2014)
@Sunil. Case I is right. Logically father's age should be more than son's age. So 4x is greater than x so its right to take son's age x and father's age 4x. Case-II is logically wrong. Let x=20 i.e father's age then Son's age will be 80 i.e 4x. How could a 20yrs father can have 80 yrs son. Hence case - I is right sons age x and fathers age 4x.

Ashok said: (Sep 15, 2014)
Take father age = x. Son age = y. Sum of father+son = 60. x+y = 60 eq(i). 6 yrs ago father age is 5 times the age of son. x-6 = 5(y-6). x-6 = 5y-30. x = 5y-30+6. x = 5y-24. Sub x value in eq(i). 5y-24+y = 60. 6y = 60+24 = 84. y = 14. Then 6 yrs after the son age = 14+6 = 20 years.

Imran Ali Korai said: (Oct 15, 2014)
Present age of son = x. Present age of father = 5x. 6 years ago. Son's age = x + 6. Father's age = 5x + 6. Sum of their ages. X+6+5x+6 = 60. 6x = 48. X = 8. Son's age = x+6 = 14. After Six Year's 14+6 = 20. Hence 20 is correct answer.

Sudha said: (Dec 11, 2014)
We can solve like this also: Father is mentioned as 'f'. Son is mentioned as 's'. Sum of father and son age ==> f+s = 60 ----- (1). Before 6 years ==> (f-6) = 5(s-6). F-5s = -24 -------------- (2). Solve equation 1 and 2 we can get the value of s = 14. The current age of son is ===> 14. After 6 year ==> 14+6 = 20.

Avinash said: (Oct 4, 2015)
In previous sum + for ago in this this sum your using - for ago what we have to use say properly.

Somya Khare said: (Oct 11, 2015)
Son = x. Father = y. Then, x+y = 60.....(1). 6 years ago. (y-6) = 5(x-6). That is y-6 = 5x-30. Therefore at present age we have y-6+6 = 5x-30+6. That is, y = 5x-24. From (1). x+5x-24 = 60. 6x = 84. x = 14. Therefore after 6 years sons age will be. 14+6 = 20.

Divya said: (Dec 8, 2015)

I'm confused with this answer. I solve like this correct me if I'm wrong. Let the present age of father = x. Let the present age of son = y. Sum of present age: x+y= 60 then equate will become: y = 60-x. 6 years ago the age of father will be 5 times the age of his son. Father: x-6. Son: y-6. Equate these 2 equation, would become: x-6 = 5(y-6). x-6 = 5y-30. By substituting the value y = 60-x: x-6 = 5(60-x)-30. x = 46 (present age of father). Substitute the age of father to y = 60-x would gives us the present age of his son. y = 60-46. y = 14 (present age his son). 14 is my answer;

Thank you!

Zulminan Ahmed said: (Jan 5, 2016)
Let father's age = X. Let son's age = Y. So, A/Q X+Y = 60 (Equation 1). But six years ago father's age was five times the age of the son. So, X-6 = 5(Y-6) (Equation 2). Now putting the value of X = 60-Y from (Equation 1) in (Equation 2). So, 60-Y-6 = 5(Y-6). So the value of Y = 14. But in question we have to find the son's age after 6 years so added 6 in 14. So, answer will be 20 years. FINE!

Kirti said: (Jan 26, 2016)
Father age = f, son age = s. Then f+s = 60; f+6 = 5(s+6). On solving s = 6; Then present age of son = s+6 = 6+6 = 12; Then after 6 years it will be = 12+6 = 18; What is wrong in that?

Siva said: (Feb 1, 2016)
6 years ago son age = x, then father = 5x. Present age of son means x+6 like that father age is 5x+6. x+6+5x+6 = 60. So x = 8, here it is. After 6 years son age will be x+6+6 = 8+6+6 = 20.

Dhinu said: (Sep 6, 2016)

Let the present age of the father is F, Son's present age is S. The sum of their ages S + F = 60. Fathers age 6 years ago (means - 6) F - 6, Sons age 6 years ago S - 6, Now given Six years ago, father's age was five times the age of the son. Six years ago, father's age: F - 6 = 5(S - 6), F - 6 = 5(S - 6) ---> Eq1 F + S = 60 ---> Eq2 by solving we get S = 14. Question is to find after(ADD) 6 years so ADD 6.

Hence, Sons's age after six years will be 20 years.

Nish said: (Oct 24, 2016)
Age of the son 6 years ago = 'X'. Age of the father 6 years ago = '5X'. At present sum of the father and son's age = (X + 6) + (5X + 6) = 60. => X = 8 which is assumed as the age of 6 years ago so, at present age of the son is X + 6 i.e 8 + 6 = 14. After 6 years age of the son will be = 14 + 6 = 20 years.

Sindhu Kalyan said: (Nov 5, 2016)
Thank you @AMIT.

Pravin Garodi said: (Nov 13, 2016)
Consider son present age is X and father present age is Y. X + Y = 60 consider this is first equation, 6 year ago father age is, (Y - 6) = 5(X - 6), 5(X - 6) = Y - 6, 5X - Y = 24 this is second equation. After solving 1 and 2 equation, X = 14, After 6 year son age is 14 + 6 = 20.

Koteswararao Chimmili said: (Nov 28, 2016)

Sum of present ages of a father and his son is 60 years. Son + Father = 60 Six years ago: Son + father = 60 - 12( six years ago means son-6 and father-6 ) Son + father = 48 -------->equation 1. Father's age was five times the age of the son. Son age x; Father age 5x; x = 5x. Son age and father age substitute in equation 1. Son + father = 48. x + 5x = 48. 6x = 48. x = 8 (x = 5x). The present age of son: Six years ago the age of son+6. 8 + 6 = 14. After 6 years, son's age will be: Son present age +6.

14 + 6 = 20.

Bharath said: (Dec 28, 2016)
@All. Let father & son's age be x&y. As said present sum of x + y = 60. & six yrs ago father's age was five times the age of his son i. e (x-6) = 5(y-6)>>>eq 1. x + y = 60>>we can ryt this as x = 60 - y. So, substitute x value in eq 1. (60 - y - 6) = 5(y - 6) 54 - y = 5y - 30 54 + 30 = 5y + y 84 = 6y. So, y = 84/6 = 14, y = 14. And y's age after 6 yrs =(y + 6). = 14 + 6 = 20yrs. So answer is D

Akash said: (Feb 28, 2017)
6 years ago their age ratio was 5x : x right? Then to find thier present age add 6yeras to both of them, Now it becomes 5x+6 : x+6. A/c data sum of their present age is equal to 60. Now. 5x+6(father's age) + x+6(son's age) =60. i.e 5x+6+x+6 = 60, 6x+12 = 60, 6x = 48, x = 8. x is son's age six years ago; Son's present age is 8 + 6 =14. Son's age after 6years from present is 14+6 = 20.

Shaila said: (Apr 17, 2017)
Thank you everyone for explaining the solution.

Akshay said: (Jun 3, 2017)
Simple Steps: The Sum of Father and Son age: F+S=60. Before 6 years condition: F-6=5(S-6); F=5S-24, Put F in F+S=60 i.e, 5S-24+S=60 ; S=14 After Six years, S=14+6 = 20.

G.Bharath Reddy said: (Sep 16, 2017)
Simple steps: Let the ages of father and be y,x; x+y+6=60; Before 6 years,fathers age was x+6=5x+6 x+6+5x+6=60; 6x+12=60; 6x=48; x=8; So,son age is 8yrs; At that moment,son age is=8+6=14yrs; After 6yrs=14+6; 20 yrs/.

Haider said: (Sep 19, 2017)
We can solve it by this method. The sum of the ages =60 six years ago we will subtract 12 years, 6 year each, then sum would be 48. divide by 6, bco s they are in the ratio of 1:5. 8 : 40 would be the answer, Add 12 years to 8 and we get 20.

Alekhya said: (Nov 9, 2017)
Father = 60-x. 6 years ago so (-) symbol if it is after 6 years means we add (+) symbol. We add 6 to both sides, (60-x)-6 = (x-6). Here ques asked father's age was five times the age of the son So, (60-x)-6 = five times of(x-6) /(x-6) is sons age)/. (60-x)-6 = 5(x-6). 54-x = 5x-30. 6x = 84. x = 84/6. x = 14. After 6 years, son's age will be: Son age x. After six years so; x+6. 14+6 = /20 years/.

Anil said: (Dec 30, 2017)
Present age of F+S=60. F=60-S. 6 years ago age of F+S=60-6-6=48-----(1) and 6years ago son age is (s-6) and father age is 5(s-6). Substitute these are in eq(1). 5(s-6)+(s-6)=48, 5s-6s+s-6=48, Present age of son is S=14. From F=60-s, =>F=60-14, Present age of father F=46. After 6years son age is S=14+6 S=20 years. After 6 years father age is F =46+6=52.

Vikas said: (Dec 30, 2017)
Let the ratio of father and son 6 years ago was 5x:x. Both father and son age's sum 6 years ago was, 60-12=48, Then, 5x+x=48, 6x=48, x=8. Father age was 5*8=40 and son's age was 8. At present father age is 40+6=46 and son's age is 8+6=14. At present father and son's age some 46+14=60. Then how the son's age is 20?

Rass said: (Apr 3, 2018)
The age of A and B three years ago were 'x' and 'y+2' years, therefore the sum of their ages 4 years hence will be? Can someone solve this?

Vidyaram Meena said: (Aug 30, 2018)

There is another way to solve the same problem. Let's suppose son age y and father age x. according to question x+y=60 ----> eqn(1). and x-6=5(y-6). x-5y=-24----> equ(2). By solving eqn(1) and eqn(2) we get y=14. From question. Then, y+6=14+6=20.

Hence after 6 years, the age of son is 20.

Gaurav Kumar said: (Apr 17, 2019)
Thank you so much for explaining the answer.

Prithiv Raj said: (Jul 6, 2019)
Let father age be x. Son be y. X+y=60, X-6=5y, Y=x-6/5. Sub y in above eq. X+x-6/5=60. 5x+x-6=300. 6x=294. X=49 father age. Sub x in above. 49+y=60. Y=11. After 6 years 11+6=17 years.

Teena Joy P J said: (Jul 30, 2019)

Here, in this question, we can see 3 periods of time(past, present, future). Take past first, ie, 6 yrs b4: son=X and dad=5X. Now take present: Son=X+6 and Dad=5X+6. Given a hint that at present their sum of ages is 60; a task made easy. X + 6 + 5X + 6 = 60, X = 8. Now take future (we have to find ans in future): After 6 more yrs: Son=X+12 and dad=5X+12 So the son will be 8+12 yrs old.

The age of son =20.

Dhanesh P G said: (Dec 5, 2019)
My solution is given by, The present sum of ages 60. So 6 years ago the sum is 48. Then the ratio is 5:1 it means 5x+x=6x=48. Then x=8 and, Age after 6 years is 40+12=52 and 8+12= 20.

Sushmitha C P said: (Jan 11, 2020)
Sum of both ages is F + S = 60 We can also write as F = 60 - S ------> Eqn 1. 6 years ago father age will be 5 times the age of son -> eq becomes F - 6 = 5 (S - 6)------> Eqn(2). Then substitute eq(1) to eq(2). Then eq becomes (60-S)-6 = 5 (S - 6). (60-S)-6 = 5S - 30, 60+30-6=5S+S, 84=6S, S = 14. Then add 6 to it (because after 6 years so)so 14 + 6 = 20.

Srujan said: (Jan 31, 2020)
Thank you all.

Naximi said: (Apr 28, 2020)
Thanks @Amit.

Isha said: (Aug 23, 2020)
Very easy to understand, Thanks @Amit.

Nikhil G said: (Oct 16, 2020)
x+y = 60 -------------> eqn1 5x-6 = y-6 => 5x = y ----------> eqn2 Equating both equation: y/5 = 60-y. y=300-20y. y=300/19. y = 14 years. After 6 years 14+6 = 20.

Abhi said: (Dec 15, 2020)
@Amit. You have already added 6 to bring question in present (x+6) & (5x+6). Now the outcome of this solution is 8yr right. This 8yr must be present age of son we have to add 6 to know future age hence, 8+6=14. How have you added 8+6+6? I didn't understand please reply.

Hassan said: (Jan 4, 2021)
Very helpful. Thanks for explaining @Amit.

M Mahd Pakistan said: (Jan 9, 2021)
Thanks @Amit.

Rituparna Pati said: (Jun 13, 2021)
@Amit. You have already added 6 to the years to convey the present years of both of them. Then why have you added another 6 years. I can't understand! Please explain it.

Mahendran Kamaraj said: (Dec 25, 2021)
Son's age= x, Father's age is y. x+y=60 -------> (1). As per 2nd statement; (y-6) = 5(x-6). 5x-y=24 ------> (2). Therefore solving equ. 1 & 2. x=14 & y = 46. 3rd condition; Son age after 6 years. 14+6= 20 years.

Hiwote End said: (Feb 14, 2022)
f+s = 60. f-6 = 5(s-6), f = 5s-30 +6, f = 5s-24, f+s = 60, 5s-24+s = 60, 6s=60+24 = 84, s = 14 but our target to find son age after 6 years. 14+6= 20.