Time and Work

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 & Explanation 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.

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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. 20 3 days 17 D. None of these Answer & Explanation 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.

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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 & Explanation 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  Time taken by both to type 110 pages = 110 x 3 hours 40 = 8 1 hours (or) 8 hours 15 minutes. 4

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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 & Explanation 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

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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 & Explanation 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.

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 & Explanation Answer: Option B Explanation: Suppose A, B and C take x, x and x days respectively to finish the work. 2 3 Then, 1 + 2 + 3 = 1 x x x 2 6 = 1 x 2  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 & Explanation Answer: Option C Explanation: (A + B)'s 1 day's work = 1 + 1 = 1 . 15 10 6 Work done by A and B in 2 days = 1 x 2 = 1 . 6 3 Remaining work = 1 - 1 = 2 . 3 3 Now, 1 work is done by A in 1 day. 15 2 work will be done by a in 15 x 2 = 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 & Explanation Answer: Option A Explanation: 2(A + B + C)'s 1 day's work = 1 + 1 + 1 = 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 = 1 - 5 = 3 . 8 8 A's 1 day's work = 1 - 1 = 1 . 16 24 48 Now, 1 work is done by A in 1 day. 48 So, 3 work will be done by A in 48 x 3 = 18 days. 8 8

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24.	A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :
	A. 4 days B. 6 days C. 8 days D. 18 days Answer & Explanation Answer: Option A Explanation: Ratio of rates of working of A and B = 2 : 1. So, ratio of times taken = 1 : 2. B's 1 day's work = 1 . 12  A's 1 day's work = 1 ; (2 times of B's work) 6 (A + B)'s 1 day's work = 1 + 1 = 3 = 1 . 6 12 12 4 So, A and B together can finish the work in 4 days.

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25.	Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?
	A. 3 : 4 B. 4 : 3 C. 5 : 3 D. Data inadequate Answer & Explanation Answer: Option B Explanation: (20 x 16) women can complete the work in 1 day.  1 woman's 1 day's work = 1 . 320 (16 x 15) men can complete the work in 1 day.  1 man's 1 day's work = 1 240 So, required ratio = 1 : 1 240 320 = 1 : 1 3 4 = 4 : 3 (cross multiplied)

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 :
	A. 4 days B. 6 days C. 8 days D. 12 days Answer & Explanation 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  (A + C)'s 1 day's work = 2 x 1 - 1 + 1 6 8 12 = 1 - 5 3 24 = 3 24 = 1 . 8 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. 10 1 days 2 Answer & Explanation Answer: Option C Explanation: (B + C)'s 1 day's work = 1 + 1 = 7 . 9 12 36 Work done by B and C in 3 days = 7 x 3 = 7 . 36 12 Remaining work = 1 - 7 = 5 . 12 12 Now, 1 work is done by A in 1 day. 24 So, 5 work is done by A in 24 x 5 = 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. 13 1 days 3 B. 15 days C. 20 days D. 26 days Answer & Explanation Answer: Option A Explanation: Work done by X in 8 days = 1 x 8 = 1 . 40 5 Remaining work = 1 - 1 = 4 . 5 5 Now, 4 work is done by Y in 16 days. 5 Whole work will be done by Y in 16 x 5 = 20 days. 4  X's 1 day's work = 1 , Y's 1 day's work = 1 . 40 20 (X + Y)'s 1 day's work = 1 + 1 = 3 . 40 20 40 Hence, X and Y will together complete the work in 40 = 13 1 days. 3 3

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29.	A and B can do a job together in 7 days. A is 1 times as efficient as B. The same job can be done by A alone in :
	A. 9 1 days 3 B. 11 days C. 12 1 days 4 D. 16 1 days 3 Answer & Explanation Answer: Option B Explanation: (A's 1 day's work) : (B's 1 day's work) = 7 : 1   =   7 : 4. 4 Let A's and B's 1 day's work be 7x and 4x respectively. Then, 7x + 4x = 1          11x = 1          x = 1 . 7 7 77  A's 1 day's work = 1 x 7 = 1 . 77 11

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30.	A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
	A. 30 days B. 40 days C. 60 days D. 70 days Answer & Explanation Answer: Option C Explanation: Let A's 1 day's work = x and B's 1 day's work = y. Then, x + y = 1 and 16x + 44y = 1. 30 Solving these two equations, we get: x = 1 and y = 1 60 60  B's 1 day's work = 1 . 60 Hence, B alone shall finish the whole work in 60 days.