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Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?

1 years ago
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Exercise :: Time and Work - General Questions

26. 

A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :

Show
A. 4 days
B. 6 days
C. 8 days
D. 12 days

Answer: Option C

Explanation:

(A + B + C)'s 1 day's work = 1 ;
6

(A + B)'s 1 day's work = 1 ;
8

(B + C)'s 1 day's work = 1 .
12

Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
(A + C)'s 1 day's work
=
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 2 x 1
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 -
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 + 1
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
6 8 12
=
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 - 5
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
3 24

So, A and C together will do the work in 8 days.

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27. 

A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:

A. 5 days
B. 6 days
C. 10 days
D.

Answer: Option C

Explanation:

(B + C)'s 1 day's work =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 + 1
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 7 .
9 12 36

Work done by B and C in 3 days =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 7 x 3
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 7 .
36 12

Remaining work =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 - 7
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 5 .
12 12

Now, 1 work is done by A in 1 day.
24

So, 5 work is done by A in
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 24 x 5
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 10 days.
12 12

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28. 

X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?
A.
B. 15 days
C. 20 days
D. 26 days

Answer: Option A

Explanation:

Work done by X in 8 days =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 x 8
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 1 .
40 5

Remaining work =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 - 1
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 4 .
5 5

Now, 4 work is done by Y in 16 days.
5

Whole work will be done by Y in
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 16 x 5
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 20 days.
4

Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
X's 1 day's work =		 1 , Y's 1 day's work = 1 .
40 20

(X + Y)'s 1 day's work =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 + 1
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 3 .
40 20 40

Hence, X and Y will together complete the work in
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 40
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 13 1 days.
3 3

Page 2

Exercise :: Time and Work - General Questions

6. 

If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:

A. 4 days
B. 5 days
C. 6 days
D. 7 days

Answer: Option A

Explanation:

Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.

Then, 6x + 8y = 1 and 26x + 48y = 1 .
10 2

Solving these two equations, we get : x = 1 and y = 1 .
100 200

(15 men + 20 boy)'s 1 day's work =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 15 + 20
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 1 .
100 200 4

Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
15 men and 20 boys can do the work in 4 days.

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7. 

A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
A. 8 hours
B. 10 hours
C. 12 hours
D. 24 hours

Answer: Option C

Explanation:

A's 1 hour's work = 1 ;
4

(B + C)'s 1 hour's work = 1 ;
3

(A + C)'s 1 hour's work = 1 .
2

(A + B + C)'s 1 hour's work =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 + 1
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 7 .
4 3 12

B's 1 hour's work =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 7 - 1
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 1 .
12 2 12

Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
B alone will take 12 hours to do the work.

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8. 

A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:

A. 15 days
B. 20 days
C. 25 days
D. 30 days

Answer: Option C

Explanation:

(A + B)'s 1 day's work = 1
10

(A + B + C)'s 1 day's work =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 + 1
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 6 = 3 . .... (i)
10 50 50 25

A's 1 day's work = (B + C)'s 1 day's work .... (ii)

From (i) and (ii), we get: 2 x (A's 1 day's work) = 3
25

Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
A's 1 day's work =		 3 .
50

Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
B's 1 day's work
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 - 3
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 2 = 1 .
10 50 50 25

So, B alone could do the work in 25 days.

Page 3

Exercise :: Time and Work - General Questions

11. 

A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?

Answer: Option C

Explanation:

B's 10 day's work =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 x 10
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 2 .
15 3

Remaining work =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 - 2
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 1 .
3 3

Now, 1 work is done by A in 1 day.
18

Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 work is done by A in
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 18 x 1
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 6 days.
3 3

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12. 

4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

Answer: Option B

Explanation:

Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.

Then, 4x + 6y = 1 and 3x + 7y = 1 .
8 10

Solving the two equations, we get: x = 11 , y = 1
400 400

Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
1 woman's 1 day's work =		 1 .
400

Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
10 women's 1 day's work =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 x 10
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 1 .
400 40

Hence, 10 women will complete the work in 40 days.

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Page 4

Exercise :: Time and Work - General Questions

16. 

X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

A. 6 days
B. 10 days
C. 15 days
D. 20 days

Answer: Option B

Explanation:

Work done by X in 4 days =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 x 4
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 1 .
20 5

Remaining work =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 - 1
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 4 .
5 5

(X + Y)'s 1 day's work =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 + 1
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 8 = 2 .
20 12 60 15

Now, 2 work is done by X and Y in 1 day.
15

So, 4 work will be done by X and Y in
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 15 x 4
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 6 days.
5 2 5

Hence, total time taken = (6 + 4) days = 10 days.

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17. 

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?
A. 11 days
B. 13 days
C.
D. None of these

Answer: Option B

Explanation:

Ratio of times taken by A and B = 100 : 130 = 10 : 13.

Suppose B takes x days to do the work.

Then, 10 : 13 :: 23 : x    
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
    x =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 23 x 13
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
    
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
    x =		 299 .
10 10

A's 1 day's work = 1 ;
23

B's 1 day's work = 10 .
299

(A + B)'s 1 day's work =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 + 10
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 23 = 1 .
23 299 299 13

Therefore, A and B together can complete the work in 13 days.

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18. 

Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
A. 7 hours 30 minutes
B. 8 hours
C. 8 hours 15 minutes
D. 8 hours 25 minutes

Answer: Option C

Explanation:

Number of pages typed by Ravi in 1 hour = 32 = 16 .
6 3

Number of pages typed by Kumar in 1 hour = 40 = 8.
5

Number of pages typed by both in 1 hour =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 16 + 8
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 40 .
3 3

Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
Time taken by both to type 110 pages =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 110 x 3
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 hours
40

= 8 1 hours (or) 8 hours 15 minutes.
4

Page 5

Exercise :: Time and Work - General Questions

21. 

A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:

A. 4 days
B. 6 days
C. 8 days
D. 12 days

Answer: Option B

Explanation:

Suppose A, B and C take x, x and x days respectively to finish the work.
2 3

Then,
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 + 2 + 3
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 1
x x x 2

Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 6 = 1
x 2

Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
x = 12.

So, B takes (12/2) = 6 days to finish the work.

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22. 

A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :
A. 8 days
B. 10 days
C. 12 days
D. 15 days

Answer: Option C

Explanation:

(A + B)'s 1 day's work =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 + 1
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 1 .
15 10 6

Work done by A and B in 2 days =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 x 2
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 1 .
6 3

Remaining work =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 - 1
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 2 .
3 3

Now, 1 work is done by A in 1 day.
15

Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 2 work will be done by a in
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 15 x 2
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 10 days.
3 3

Hence, the total time taken = (10 + 2) = 12 days.

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23. 

A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?
A. 18 days
B. 24 days
C. 30 days
D. 36 days

Answer: Option A

Explanation:

2(A + B + C)'s 1 day's work =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 + 1 + 1
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 15 = 1 .
30 24 20 120 8

Therefore, (A + B + C)'s 1 day's work = 1 = 1 .
2 x 8 16

Work done by A, B, C in 10 days = 10 = 5 .
16 8

Remaining work =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 - 5
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 3 .
8 8

A's 1 day's work =
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 1 - 1
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 1 .
16 24 48

Now, 1 work is done by A in 1 day.
48

So, 3 work will be done by A in
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 48 x 3
Can do a piece of work in 10 days and B can do it in 15 days in how many days will A and B together do the same work?
 = 18 days.
8 8

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