30 + Interview Questions in Time and Work in Aptitude Page 1 InterviewSolution

1.	A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Answer» C's 1 day's work = 1 - 1 + 1 = 1 - 7 = 1 . 3 6 8 3 24 24 A's wages : B's wages : C's wages = 1 : 1 : 1 = 4 : 3 : 1. 6 8 24 C's share (for 3 days) = Rs. 3 x 1 x 3200 = Rs. 400. 24

Discussion

2.	10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
Answer» 1 woman's 1 day's work = 1 70 1 child's 1 day's work = 1 140 (5 women + 10 children)'s day's work = 5 + 10 = 1 + 1 = 1 70 140 14 14 7 5 women and 10 children will complete the work in 7 days.

Discussion

3.	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?
Answer» 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.

Discussion

4.	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?
Answer» 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.

Discussion

5.	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?
Answer» 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

Discussion

6.	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:
Answer» 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

Discussion

7.	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» B's 10 day's work = 1 x 10 = 2 . 15 3 Remaining work = 1 - 2 = 1 . 3 3 Now, 1 work is done by A in 1 day. 18 1 work is done by A in 18 x 1 = 6 days. 3 3

Discussion

8.	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» 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 1 woman's 1 day's work = 1 . 400 10 women's 1 day's work = 1 x 10 = 1 . 400 40 Hence, 10 women will complete the work in 40 days.

Discussion

9.	A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work?
Answer» (A + B)'s 20 day's work = 1 x 20 = 2 . 30 3 Remaining work = 1 - 2 = 1 . 3 3 Now, 1 work is done by A in 20 days. 3 Therefore, the whole work will be done by A in (20 x 3) = 60 days.

Discussion

10.	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 :
Answer» (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.

Discussion

11.	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:
Answer» (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

Discussion

12.	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?
Answer» 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

Discussion

13.	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 :
Answer» (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

Discussion

14.	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?
Answer» 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.

Discussion

15.	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:
Answer» 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 = 15 + 20 = 1 . 100 200 4 15 men and 20 boys can do the work in 4 days.

Discussion

16.	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?
Answer» 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 = 1 + 1 = 7 . 4 3 12 B's 1 hour's work = 7 - 1 = 1 . 12 2 12 B alone will take 12 hours to do the work.

Discussion

17.	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:
Answer» 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.

Discussion

18.	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 :
Answer» (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.

Discussion

19.	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?
Answer» 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

Discussion

20.	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 :
Answer» 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.

Discussion

21.	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?
Answer» (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)

Discussion

22.	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:
Answer» (A + B)'s 1 day's work = 1 10 C's 1 day's work = 1 50 (A + B + C)'s 1 day's work = 1 + 1 = 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 A's 1 day's work = 3 . 50 B's 1 day's work 1 - 3 = 2 = 1 . 10 50 50 25 So, B alone could do the work in 25 days.

Discussion

23.	A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
Answer» Whole work is done by A in 20 x 5 = 25 days. 4 Now, 1 - 4 i.e., 1 work is done by A and B in 3 days. 5 5 Whole work will be done by A and B in (3 x 5) = 15 days. A's 1 day's work = 1 , (A + B)'s 1 day's work = 1 . 25 15 B's 1 day's work = 1 - 1 = 4 = 2 . 15 25 150 75 So, B alone would do the work in 75 = 37 1 days. 2 2

Discussion

24.	A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?
Answer» (P + Q + R)'s 1 hour's work = 1 + 1 + 1 = 37 . 8 10 12 120 Work done by P, Q and R in 2 hours = 37 x 2 = 37 . 120 60 Remaining work = 1 - 37 = 23 . 60 60 (Q + R)'s 1 hour's work = 1 + 1 = 11 . 10 12 60 Now, 11 work is done by Q and R in 1 hour. 60 So, 23 work will be done by Q and R in 60 x 23 = 23 hours 2 hours. 60 11 60 11 So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.

Discussion

25.	A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :
Answer» A's 1 day's work = 1 ; 15 B's 1 day's work = 1 ; 20 (A + B)'s 1 day's work = 1 + 1 = 7 . 15 20 60 (A + B)'s 4 day's work = 7 x 4 = 7 . 60 15 Therefore, Remaining work = 1 - 7 = 8 . 15 15

Discussion

26.	A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
Answer» (A + B + C)'s 1 day's work = 1 , 4 A's 1 day's work = 1 , 16 B's 1 day's work = 1 . 12 C's 1 day's work = 1 - 1 + 1 = 1 - 7 = 5 . 4 16 12 4 48 48 So, C alone can do the work in 48 = 9 3 days. 5 5

Discussion

27.	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:
Answer» 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's 1 day's work = 1 30 B's 1 day's work = 1 90 (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

Discussion

28.	P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?
Answer» P can complete the work in (12 x 8) hrs. = 96 hrs. Q can complete the work in (8 x 10) hrs. = 80 hrs. P's1 hour's work = 1 and Q's 1 hour's work = 1 . 96 80 (P + Q)'s 1 hour's work = 1 + 1 = 11 . 96 80 480 So, both P and Q will finish the work in 480 hrs. 11 Number of days of 8 hours each = 480 x 1 = 60 days = 5 5 days. 11 8 11 11

Discussion

29.	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:
Answer» 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.

Discussion

30.	A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
Answer» A's 2 day's work = 1 x 2 = 1 . 20 10 (A + B + C)'s 1 day's work = 1 + 1 +1 = 6 = 1 . 20 30 60 60 10 Work done in 3 days = 1 + 1 = 1 . 10 10 5 Now, 1 work is done in 3 days. 5 Whole work will be done in (3 x 5) = 15 days.

Discussion

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