# Unitary & Methods

# Time and Work Aptitude Concepts and Formulas

## Points to Remember

1) If a man can do a piece of work in n days, work done by him in one day =part of total work or he will finish work in one day.

2) If a man completes work in one day, he will complete the entire work in n days.

3) If A can complete a piece of work in X days and B can complete the same work in Y days, both A and B working together can finish the same work indays.

4) If A is thrice as good as workman as B or A can work three times faster than B, the ratio of work done by A and B for the same duration of time will be = 3 : 1. And the ratio of time taken by A and B to finish the same amount of work will be = 1: 3.

5) A, B and C can do a work in D1, D2 and D3 days respectively. If they work for X1, X2 and X3 days respectively;

- Work done by A in X1 days =
- Work done by B in X2 days =
- Work done by C in X3 days =

6) If A, B, C can do a piece of work in X, Y, and Z days respectively, if they work together they can do the same work indays.

7) A and B working together can do a work in X days. If A alone can do the same work in Y days, B alone can do the same work indays.

8) A and B working together can finish a piece of work in X days, B and C working together can finish the same work in Y days and C and A in Z days. Then;

- A, B and C working together will finish the work in days.
- A alone will finish the work in =days.
- B alone will finish the work in =days.
- C alone will finish the work in =days.

9) A can do a work in X days. If B is P times efficient than A, A and B working together can do the work indays.

10) A and B working together can complete a work in X days. If B is P times efficient than A;

- A alone can complete the work in (P + 1) X days.
- B alone can complete the work in X days.

11) P working alone takes X days more to do a work than P and Q working together takes to do the same work. And, Q working alone takes Y days more to do the same work than P and Q working together takes to finish the same work. Then P and Q working together can finish the same work in √XY days.

12) A is P times more efficient than B and able to finish the work in X days less than B, then

A and B working together can finish the work indays.

- A alone can finish the work indays.
- B alone can finish the work indays.

13) If A completes part of a work in X days,part of the same work he can complete indays.

14) There are two groups of workers with same efficiency. In one group M1 workers can do W1 work in D1 days or time. In the second group M2 workers can do W2 work in D2 days or time.Then;

M1 D1 W2 = M2 D2 W1

15) There are two groups of workers with the same efficiency. In one group M1 workers can do W1 work in D1 time or days working T1 hours a day. In the second group, M2 workers can do W2 work in D2 time or days working T2 hours in a day. Then;

M1 D1 T1 W2 = M2 D2 T2 W1

- If the efficiency of the workers is different in these groups i.e. E1 and E2,; M1 D1 T1 E1W2 = M2 D2 T2E2W1
- Also remember that efficient person takes less time to complete a given work. So, we can say that efficiency (E) is indirectly proportional to the number of days (D) taken to complete the given work.

Therefore, ED = constant

E1D1 = E2D2

More men will take fewer days and fewer men will take more days to complete a given work.

16) Wages are directly proportional to the work done by the individual and inversely proportional to the time taken by the individual.

Total wages = One person’s one day’s wage * number of persons* number of days

A’s share : B’s share : C’s share = B’s time*C time : A’s time*C’s time : A’s time * B’s time.

1) Worker A completes a task in 8 days, and worker B completes the same task in 10 days. If both A and B work together, in how many days they will complete the task?

- days.
- days.
- days.
- days.

2) Vikas and Mohan working together can complete a work in 6 days. If Vikas alone completes the same work in 10 days, in how many days Mohan alone can complete the same work?

- 13 days
- 14 days
- 15 days
- 16 days

3) A can do a work in 10 days and B can do the same work in 15 days. If they start working together but stop working after four days, find the fraction of the work that is left.

4) Peter is twice as good as workman as Tom. When they work together they can finish a task in 16 days. If Tom works alone, in many days he will complete the task?

- 46 days
- 48 days
- 50 days
- 52 days

5) A can do a job in 12 days and B can do the same job in 10 days. With the help of C they can do the same job in 4 days. In how many days C alone can do this job?

- 15 days
- 14 days
- 13 days
- 12 days

6) A, B, C can do a job in 10, 20 and 40 days respectively. In how many days A can complete the job if he is assisted by B and C on every third day?

- 8 days
- 7 days
- 9 days
- 6 days

7) If 5 men can colour 50-meter long cloth in 5 days, in many days 4 men can color a 40-meter long cloth?

- 5 days
- 6 days
- 4 days
- 3 days

8) If 4 men can finish 4 times of a work in 4 days, in how many days 6 men can finish the 6 times of same work ?

- 3 days
- 4 days
- 5 days
- 6 days

9) A can do a piece of work in 10 days. B is 50% more efficient than A. In how many days B alone can do the same job?

- 6.2 days
- 6.6 days
- 7 days
- 7.2 days

10) A can do a job in 30 days. B alone can do the same job in 20 days. If A starts the work and joined by B after 10 days, in how many days the job will be done?

- 15 days
- 16 days
- 17 days
- 18 days

11) A can do a piece of work in 6 days working 8 hours a day. B can do the same work in 4 days working 6 hours a day. If they work together 8 hours a day, in how many days they will do this work?

- 3 days
- 3.5 days
- 2 days
- 2.5 days

12) A can finish a work in 6 days and B can finish the same work in 8 days. A and B charge Rs. 2800 for the work. If with the help of C they complete the work in 3 days, how much they will pay to C?

- Rs. 350
- Rs. 345
- Rs. 340
- Rs. 320

13) 5 men undertook a piece of work and finished half the work in 18 days if two men drop out, in how many days the remaining work will be completed?

- 30 days
- 32 days
- 34 days
- 36 days

14) If 5 workers can paint a house in 9 days, in how many days 3 workers can complete the same task?

- 13 days
- 14 days
- 15 days
- 16 days

15) A group of workers undertakes a task. They can complete the task in 30 days. If 5 of them did not turn for the work and the remaining workers complete the task in 40 days, find the original number of workers.

- 25 days
- 23 days
- 21 days
- 20 days

16) 40 men can paint a building in 15 days working 4 hours a day. In how many days 30 men working 5 hours a day will complete the work?

- 14 days
- 15 days
- 16 days
- 17 days

17) A certain number of men can do a piece of work in 50 days. If there were 6 men more the same work could be done in 10 days less. Find the original number of men.

- 21 men
- 22 men
- 23 men
- 24 men

18) A is twice as good as workman as B so he can do a work in 40 days less than B. If they work together, in how many days they can do the work?

- 80/4 days
- 80/5 days
- 80/3 days
- 80/6 days

19) A is twice as good as workman as B and working together they can do a piece of work in 20 days. If A alone works, in how many days he will do the work?

- 30 days
- 33 days
- 37 days
- 40 days

20) 3 workers can do a piece of work in 20 days. If one of them works only for half time in a day, in how many days the work will be done?

- 24 days
- 20 days
- 22 days
- 23 days

21) A can finish the job at the same time in which B and C together do it. If A and B together can finish the work in 10 days and C alone can do the work in 50 days, how many days B will take to complete the same job?

- 20 days
- 22 days
- 22(1/2) days
- 25 days

22) A and B working together can finish a work in 12 days, B and C working together can finish the work in 16 days. If A works for 5 days, B works for 7 days, and C completes the remaining work in 13 days, C alone can complete the work in how many days?

- 22 days
- 24 days
- 26 days
- 28 days

23) A can finish a work in 10 days and B can finish the same work in 15 days. If they work alternatively, find the time taken to finish the job.

- 14 days
- 15 days
- 12 days
- 14.5 days

24) A, B, and C individually can finish a job in 10, 15, and 30 days respectively. If A starts the work and continues until the end, B and C work alternatively, in how many days work will be done?

- 6 days
- 4 days
- 4[1/3] days
- 6[3/5] days

25) A can finish a work in 10 days, B can finish the same work in 15 days, and C can finish it in 30 days. All three start working together, but after some days A leaves the job, then after one day B also left the job. C completes the remaining job in 3 days. Find the number of working days of B.

- 4 days
- 5 days
- 6 days
- 7 days