Time and Work Multiple Choice Questions
Practice MCQ question on Time and Work
1. Raju can do 25% of a piece of work in 5 days. How many days will he take to complete the work ten times?
Solution:-He will complete the work in 20 days. Hence, he will complete ten times the work in 200 days.
2. 6 men can do a piece of work in 12 days. How many men are needed to do the work in 18 days?
Solution:-6 men for 12 days means 72 man-days. This would be equal to 4 men for 18 days.
3. Nishu and Archana can do a piece of work in 10 days and Nishu alone can do it in 12 days. In how many days can Archana do it alone?
Solution:-N + A = 10% N = 8.33% Hence A = 1.66% Æ 60 days.
4. Baba alone can do a piece of work in 10 days. Anshu alone can do it in 15 days. If the total wages for the work is $50. How much should Baba be paid if they work together for the entire duration of the work?
Solution:-The ratio of the wages will be the inverse of the ratio of the number of days required by each to do the work. Hence, the correct answer will be 3:2 ->$30
5. 4 men and 3 women finish a job in 6 days, and 5 men and 7 women can do the same job in 4 days. How long will 1 man and 1 woman take to do the work?
Solution:-24 man days + 18 women days = 20 man days + 28 woman days Æ 4 man days = 10 woman days. Æ 1 man day = 2.5 woman days Total work = 24 man days + 18 woman days = 60 woman days + 18 woman days = 78 woman days. Hence, 1 man + 1 woman = 3.5 women can do it in 78/3.5 = 156/7 = 22(2/7) days.
6.If 8 boys and 12 women can do a piece of work in 25 days, in how many days, can the work be done by 6 boys and 11 women working together?
Solution:-The data is insufficient.
7.A can do a piece of work in 10 days and B can do the same work in 20 days. With the help of C, they finish the work in 5 days. How long will it take for C alone to finish the work?
Solution:-A = 10%, B = 5% and Combined work is 20%. Hence, C’s work is 5% and will require 20 days.
8.A can do a piece of work in 20 days. He works at it for 5 days and then B finishes it in 10 more days. In how many days will A and B together finish the work?
Solution:-In 5 days, A would do 25% of the work. Since B finishes the remaining 75% work in 10 days, we can conclude that B’s work in a day = 7.5% Thus, (A + B) = 12.5% per day. Together they would take 100/12.5 = 8 days.
9.A and B undertake to do a piece of work for $100. A can do it in 5 days and B can do it in 10 days. With the help of C, they finish it in 2 days. How much should C be paid for his contribution?
Solution:-A = 20%, B = 10% and A + B + C = 50%. Hence, C = 20%. Thus, in two days, C contributes 40% of the total work and should be paid 40% of the total amount.
10.Twenty workers can finish a piece of work in 30 days. After how many days should 5 workers leave the job so that the work is completed in 35 days?
Solution:-Total man-days required = 600 man-days. If 5 workers leave the job after ‘n’ days, the total work would be done in 35 days. We have to find the value of ‘n’ to satisfy: 20 x n + (35 – n) x 15 = 600. Solving for n, we get 20n – 15n + 35 x 15 = 600 5n = 75 n = 15
11. Ajay and Vijay together can do a piece of work in 6 days. Ajay alone does it in 10 days. What time does Vijay require to do it alone?
Solution:- A + V = 16.66% and A = 10% Æ V = 6.66%. Consequently Vijay would require 100/6.66 = 15 days to do it alone.
12. A cistern is normally filled in 5 hours. However, it takes 6 hours when there is a leak in its bottom. If the cistern is full, in what time shall the leak empty it?
Solution:- The rate of filling will be 20% and the net rate of the filling (including the leak) is 16.66%. Hence, the leak accounts for 3.33% per hour, i.e., it will take 30 hours to empty the tank.
13. Pipe A and B running together can fill a cistern in 6 minutes. If B takes 5 minutes more than A to fill the cistern, then the time in A and B will fill the cistern separately what time?
Solution:- A + B = 16.66%. From here solve this one using the options. Option (c) fits the situation as it gives us A’s work = 10%, B’s work = 6.66% as also that B takes 5 minutes more than A
14. A can do a work in 18 days, B in 9 days, and C in 6 days. A and B start working together and after 2 days C joins them. In how many days will the job be completed?
Solution:- A + B = 5.55 + 11.11 = 16.66. In two days, 33.33% of the work will be done. C adds 16.66% of work to that of A and B. Hence, the rate of working will go to 33.33%. At this rate, it would take 2 more days to complete the work. Hence, in total it will take 4 days to complete the entire work.
15. 24 men working 8 h a day can finish a work in 10 days. Working at a rate of 10 h a day, the number of men required to finish the work in 6 days is
Solution:- 24 x 8 x 10 = N x 10 x 6 -> N = 32
16. A certain job was assigned to a group of men to do it in 20 days. But 12 men did not turn up for the job and the remaining men did the job in 32 days. The original number of men in the group was
Solution:- n x 20 = (n – 12) x 32 -> n = 32.
17. 12 men complete a work in 18 days. 6 days after they had started working, 4 men join them. How many more days will all of them take to complete the remaining work?
Solution:- 12 x 18 = 12 x 6 + 16 x t -> t = 9
18. A takes 5 days more than B to do a certain job and 9 days more than C; A and B together can do the job at the same time as C. How many days A would take to do it?
Solution:- (A + B)’s work = C’s work. Also if A takes ‘a’ days B would take ‘a – 5’ days and C would take ‘a – 9’ days. Solving through options, option ‘c’ fits. A (15 days) -> A’s work = 6.66% B (10 days) -> B’s work = 10% C (6 days) -> C’s work = 16.66%
19. A cistern is normally filled in 6 h but takes 4 h longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in how much time?
Solution:- The cistern fills in 6 hours normally, which means that the rate of filling is 16.66% per hour. With the leak in the bottom, the rate of filling becomes 10% per hour (as it takes 10 hours to fill with the leak). This means that the leak drains out water at the rate of 6.66% per hour. This in turn means that the leak would take 100/6.66 = 15 hours to drain out the entire cistern.
20. If three taps are open together, a tank is filled in 10 h. One of the taps can fill in 5 h and another in 10 h. At what rate does the 3rd pipe work?
Solution:- Since the net work of the three taps is 10% and the first and second do 20% + 10% = 30%. Hence, the third pipe must be a waste pipe emptying at the rate of 20% per hour. Hence, the waste pipe will take a total of 5 hours to empty the tank
21. Arun and Vinay together can do a piece of work in 7 days. If Arun does twice as much work as Vinay in a given time, how long will Arun alone take to do the work.
Solution:- Let the time taken by Arun be ‘t’ days. Then, time taken by Vinay = 2t days. 1/t + 1/2t = 1/7 -> t = 10.5
22. Subhash can copy 50 pages in 10 hours; Subhash and Prakash together can copy 300 pages in 40 hours. In how much time can Prakash copy 30 pages?
Solution:- . Subhash can copy 200 pages in 40 hours (reaction to the first sentence). Hence, Prakash can copy 100 pages in 40 hours. Thus, he can copy 30 pages in 30% of the time, i.e., 12 hours.
23. X number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. What is the original number of men?
Solution:- .30X = 20 (X + 6) -> 10X = 120 -> X = 12
24.. Sashi can do a piece of work in 25 days and Rishi can do it in 20 days. They work for 5 days and then Sashi goes away. In how many more days will Rishi finish the work?
Solution:- Sashi = 4%, Rishi = 5%. In five days, they do a total of 45% work. Rishi will finish the remaining 55% work in 11 more days.
25. Raju can do a piece of work in 10 days, Vicky in 12 days and Tinku in 15 days. They all start the work together, but Raju leaves after 2 days and Vicky leaves 3 days before the work is completed. In how many days is the work completed?
Solution:- ?
26.Sambhu can do 1/2 of the work in 8 days while Kalu can do 1/3 of the work in 6 days. How long will it take for both of them to finish the work?
Solution:- Sambhu requires 16 days to do the work while Kalu requires 18 days to do the work. (1/16 + 1/18) x n = 1 n = 288/34 = 144/17
27. Manoj takes twice as much time as Anjay and thrice as much as Vijay to finish a piece of work. Together they finish the work in 1 day. What is the time taken by Manoj to finish the work?
Solution:- Let Anjay take 3t days, Vijay take 2t days and Manoj take 6t days in order to complete the work. Then we get: 1/3t + 1/2t + 1/6t = 1 -> t = 1. Thus, Manoj would take 6t = 6 days to complete the work.
28. An engineer undertakes a project to build a road 15 km long in 300 days and employs 45 men for the purpose. After 100 days, he finds only 2.5 km of the road has been completed. Find the (approx.) number of extra men he must employ to finish the work in time.
Solution:- ?
29. Apurva can do a piece of work in 12 days. Apurva and Amit complete the work together and were paid $54 and $81 respectively. How many days must they have taken to complete the work together?
Solution:- . the ratio of money given to Apurva and Amit is 2:3, their work done would also be in the same ratio. Thus, their time ratio would be 3:2 (inverse of 2:3). So, if Apurva takes 12 days, Amit would take 8 days and the total number of days required (t) would be given by the equation: (1/12 + 1/8)t = 1 -> t = 24/5 = 4.8 days
30. Raju is twice as good as Vijay. Together, they finish the work in 14 days. In how many days can Vijay alone do the same work?
Solution:- . Raju being twice as good a workman as Vijay, you can solve the following equation to get the required answer: 1/R + 1/2R = 1/14. Solving will give you that Vijay takes 42 days.
31. Ashok and Mohan can do a piece of work in 12 days. Mohan and Binod together do it in 15 days. If Ashok is twice as good a workman as Binod. In how much time will Mohan alone can do the work?
Solution:- A + M = 8.33, M + B = 6.66 and A = 2B -> A’s 1 days work = 3.33%, M’s = 5% and B’s = 1.66%. Mohan would require 100/5 = 20 days
32. Ajay and Vijay can do a piece of work in 28 days. With the help of Manoj, they can finish it in 21 days. How long will Manoj take to finish the work all alone?
Solution:- Ajay + Vijay = 1/28 and Ajay + Vijay + Manoj =1/21. Manoj = 1/21 – 1/28 = 1/84. Manoj will take 84 days to do the work.
33. Anju, Manju and Sanju together can reap a field in 6 days. If Anju can do it alone in 10 days and Manju in 24 days. In how many days will Sanju alone be able to reap the field?
Solution:- Total work of Anju, Manju and Sanju = 16.66% Anju’s work = 10% Manju’s work = 4.166% Sanju’s work = 2.5% So Sanju can reap the field in 40 days.
34. In a fort there was sufficient food for 200 soldiers for 31 days. After 27 days 120 soldiers left the fort. For how many extra days will the rest of the food last for the remaining soldiers?
Solution:- After 27 days, food left = 4 ¥ 200 = 800 soldier days worth of food. Since, now there are only 80 soldiers, this food would last for 800/80 = 10 days. Number of extra days for which the food lasts = 10 – 4 = 6 days.
35. Anmol is thrice as good a workman as Vinay and therefore is able to finish the job in 60 days less than Vinay. In how many days will they finish the job working together?
Solution:- Interpret the starting statement as: Anmol takes 30 days and Vinay takes 90 days. Hence, the answer will be got by: (1/30 + 1/90) * n = 1 n=22.5
36. Ajay, Vijay and Sanjay are employed to do a piece of work for $529. Ajay and Vijay together are supposed to do 19/23 of the work and Vijay and Sanjay together 8/23 of the work. How much should Ajay be paid?
Solution:- ?
37. 15 men could finish a piece of work in 210 days. But at the end of 100 days, 15 additional men are employed. In how many more days will the work be complete?
Solution:- Total work = 15 x 210 = 3150 mandays. After 100 days, work done = 15 x 100 = 1500 mandays. Work left = 3150 – 1500 = 1650 mandays. This work has to be done with 30 men working each day. The number of days (more) required = 1650/30 = 55 days.
38. Ajay and Vijay undertake to do a piece of work for $200. Ajay alone can do it in 24 days while Vijay alone can do it in 30 days. With the help of Pradeep, they finish the work in 12 days. How much should Pradeep get for his work?
Solution:- Ajay’s daily work = 4.1666%, Vijay’s daily work = 3.33% and the daily work of all the three together is 8.33%. Hence, Pradeep’s daily work will be 0.8333%. Hence, he will end up doing 10% of the total work in 12 days. This will mean that he will be paid $20.
39. 30 men working 5 h a day can do a work in 16 days. In how many days will 20 men working 6 h a day do the same work?
Solution:- . Work equivalence method: 30 x 5 x 16 = 20 x 6 x n Gives the value of n as 20 days
40. A can do a work in 10 days and B can do the same work in 20 days. They work together for 5 days and then A goes away. In how many more days will B finish the work?
Solution:- . A’s rate of working is 10 per cent per day while B’s rate of working is 5 per cent per day. In 5 days they will complete 75 per cent work. Thus the last 25 per cent would be done by B alone. Working at the rate of 5 per cent per day, B would do the work in 5 days.
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