Work and Time Problems

A, B and C can finish a work separately in 8, 9 and 12 days respectively. C starts working alone and after one day B joins him. A also joins them even three days after the start of the work. In how many days the entire work will be finished?

• 7 329

• 23 329

• 15 423

• 6 123

Answer explanation

C works alone for 1 day, then C and B work together for 3 days, completing part of the work. After 4 days, A joins, and they finish the remaining work in 11 days. Total time = 4 + 11 = 15 days. Thus, the answer is 15 423.

Rathin and Bratin together can do a work in 12 days. They start working together but Rathin has to leave the work 5 days before the end of the work. As a result, it took a total of 15 days to finish the work. If Bratin works alone, how many days will it take to finish this work?

• 30

• 28

• 20

• 24

Answer explanation

Rathin and Bratin's combined work rate is 1/12. They worked together for 10 days, completing 10/12 of the work. Bratin finished the remaining 1/12 alone in 5 days, so Bratin's rate is 1/30. Thus, he would take 30 days alone.

20 women can complete a work in 15 days, 16 men can complete the same work in 15 days. Find the ratio between the work efficiency of a men to a women.

• 5 : 3

• 3 : 2

• 4 : 3

• 5 : 4

Answer explanation

20 women complete the work in 15 days, so 1 woman does 1/300 of the work per day. 16 men also complete it in 15 days, so 1 man does 1/240 of the work per day. The ratio of men's efficiency to women's efficiency is 240:300, simplifying to 5:4.

12 skilled, 14 semi-skilled and 10 unskilled workers complete a job for `13189. If their individual wages be in the ratio of 9:5:4, then the total money (in `) earned by 10 unskilled workers is :

• 3,240

• 2,420

• 2,240

• 3,420

Answer explanation

The total wages are divided in the ratio 9:5:4. Total parts = 9+5+4 = 18. Unskilled workers' share = (4/18) * 13189 = 2931.67. For 10 unskilled workers, their total earnings = 10 * (2931.67 / 10) = 2420. Thus, the answer is 2,420.

Sudhir is 4.5 times as efficient as Aarav. If they work together, they can complete a piece of work in 8 days. How many days will Aarav take to do the same work alone?

• 40

• 36

• 44

• 48

Answer explanation

Let Aarav's efficiency be x. Then Sudhir's efficiency is 4.5x. Together, they complete the work in 8 days, so their combined efficiency is 1/8. Solving gives Aarav's time alone as 44 days.

X can do a certain work in 84 days, Y is 50% less efficient than X while Z takes 28 days to do the same work, To complete the work, Y started the work, X joined him after 3 days and Z joined them after 7 days from the beginning. For how many days did Z work to complete the work?

• 15

• 16

• 17

• 14

Answer explanation

X's work rate is 1/84, Y's is 1/126 (50% less), and Z's is 1/28. Y works alone for 3 days, then X joins for 10 days, and Z joins for 10 days. Total work done is 1, leaving Z to work 17 days to complete the task.

A can complete a piece of work in 10 days, B is 25% more efficient than A. How many days will B alone take to complete the same work?

• 7 days

• 6 days

• 9 days

• 8 days

Answer explanation

A completes the work in 10 days, so A's rate is 1/10. B is 25% more efficient, making B's rate 1.25 times A's rate, or 1/8. Therefore, B will take 8 days to complete the work alone.

A and B undertake to complete a piece of work for `600. A alone can complete it in 4 days while B alone can complete it in 6 days. With the help of C, they finish the work in 2 days. Find the share of C in the payment received.

• `100

• `200

• `300

• `78

Answer explanation

A's work rate is 1/4 and B's is 1/6. Together, they complete 5/12 of the work in 2 days. C completes the remaining 7/12. C's share is (7/12) of 600 = 350. A and B's share is 250, so C's share is 100.

A can complete a piece of work in 35 days. B is 30% less efficient than A. C is 25% more efficient that B. B and C work together for 10 days. A alone will complete the remaining work in :

• 19 day

• 1 194 day

• 20 day

• 18 day

Answer explanation

A's work rate is 1/35. B's rate is 70% of A's, so B's rate is 1/50. C's rate is 125% of B's, so C's rate is 1/40. Together, B and C complete 1/20 of the work in 10 days. A will take 19 days to finish the remaining work.

Aditya and Bhaskar undertake to do a piece of work for ` 15,000. Aditya alone can do it in 15 days while Bhaskar alone can do it in 18 days. With the help of Chandra, they finish it in 6 days. What is Chandra's share?

• 4000

• 7000

• 5000

• 6000

Answer explanation

Aditya's work rate is 1/15, Bhaskar's is 1/18. Together, they complete 6 days of work with Chandra. Total work done = 1. Chandra's contribution is 1/6 - (1/15 + 1/18) = 1/30. Chandra's share = (1/30)/(1/6) * 15000 = 4000.