Time and work

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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 = 1 x 4 = 1 .
20 5

 

Remaining work = 1 – 1 = 4 .
5 5

 

(X + Y)’s 1 day’s work = 1 + 1 = 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 15 x 4 = 6 days.
5 2 5

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

20 3 days
17
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     =>     x = ( 23 x 13 )     =>     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 = ( 1 + 10 ) = 23 = 1 .
23 299 299 13

Therefore, A and B together can complete the work in 13 days.
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 = ( 16 + 8 ) = 40 .
3 3

 

Therefore Time taken by both to type 110 pages = ( 110 x 3 ) hours
40

 

= 8 1 hours (or) 8 hours 15 minutes.
4
19. A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:
A.
1 day
24
B.
7 day
24
C.
3 3 days
7
D. 4 days

Answer: Option C

Explanation:

 

Formula: If A can do a piece of work in n days, then A’s 1 day’s work = 1 .
n

 

(A + B + C)’s 1 day’s work = 1 + 1 + 1 = 7 .
24 6 12 24
Formula: If A’s 1 day’s work = 1 , then A can finish the work in n days.
n

 

So, all the three together will complete the job in 24 days = 3 3 days.
7 7
20. Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:
A. 15 B. 16
C. 18 D. 25

Answer: Option B

Explanation:

 

Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4.

Suppose Tanya takes x days to do the work.

 

5 : 4 :: 20 : x    x = 4 x 20
5

x = 16 days.

Hence, Tanya takes 16 days to complete the work.

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