Time & Work (Selective Placement Questions)

1. 5 men working 6 hours a day can make 10 toys in 6 days. Then in how many days 12 men working 8 hours per day can make 16 toys?

Ans: 3 days.

(Points to note in these types of questions:

More work, more days. More hours, less number of days, More men, less number of days and conversely the same applies.)

The easy way of answering the above question is to segment the given information keeping the one that is to be arrived at the end.

Men Toys Hours Days

5 10 6 6

12 16 8 x (Now relate each segment with the last keeping the above in mind)

X = 6 x 5/12 x 16/10 x 6/8 —– Reducing we get X = 3 days.

2. 12 men and 16 boys can do a piece of work in 5 days. 13 men and 24 boys can do the same work in 4 days. How long will 7 men and 10 boys take to do the same work?

Ans: 8 1/3 days.

12 M + 16 B = 5 days In 1 day —— 1/12 M + 1/16 B = 1/5 —– (i)

13 M + 24 B = 4 days In 1 day —— 1/13 M + 1/24 B = 1/4 —– (ii) Equating both (i) and (ii)

We get

60 M + 80 B = 52 M + 96 B -> 8 M = 16B -> 1 M = 2B

7M + 10B -> 7M + 5M = 12M. From Equation (i) we find – 12M + 8 M = 20M takes 5 days.

Hence 12 M will take —– 5 x 20/12 = 8 1/3 days.

3. If 5 men and 3 boys can reap 23 acres in 4 days and 3 men and 2 boys can reap 7 acres in 2 days then how many boys should help 7 men reap 45 acres in 6 days?

Ans: 2 boys.

Let ‘m’ and ‘b’ be unknown work done by a man and a boy in one day. Thus we now have

4 x (5m + 3b) = 23 ——- (i) and

2 x (3m + 2b) = 7 ——–(ii)

Equating the two we get —- 20m + 12b = 23 —— (i) and

6m + 4b = 7 ——(ii)

Multiplying (ii) by 3 and subtracting from (i) we get — 2m = 2 and one ‘m’ = 1

Substituting this value of ‘m’ in equation (ii) we get

2 x (3*1 + 2b)= 7 —– 6 + 4b = 7 -> 4b = 1 and b = 1/4

Thus we now have — 1man in one day can reap 1 acre and 1boy in one day can reap 1/4 acre.

Hence, 7 men in 6 days will reap —- 7x1x6 = 42 acres.

Total acres to be reaped is 45 acres and the boys in 6 days will have to reap 3 acres.

So the number of boys required to reap in one day —– 3/ (1/4 *6) -> 2

Hence, 2 boys will have to assist the 7 men in reaping 45 acres of land in 6 days.

4. A and B are working on your car. A alone can complete the work in six hours while B takes eight hours to complete the same work. A and B together start the work and after 2 hours A leaves to attend some other work. In how much more time B will be able to complete the job?

Ans: 3 1/3 hours.

A in one hour can do —– 1/6 job. In 2 hours can do —- 2/6 -> 1/3 job.

B in one hour can do —– 1/8 job. In 2 hours can do —- 2/8 -> 1/4 job.

Thus in 2 hours A & B together would have completed —– 1/3 + 1/4 = 7/12 work.

The remaining work is — 1 – 7/12 = 5/12. This will have to be completed by B alone.

B will take —– (5/12) / (1/8) —- 3 1/3 hours.

5. A and B together can finish a job in T days. A alone can complete the job in (T+5) days while B takes (T+45) days to finish the job. What is the value of T?

Ans: 15 days

A in one day will do –—- 1/T+5 work.

B in one day will do —— 1/T+45 work.

Thus we have an equation ——————- 1/T+5 + 1/T+45 = 1/T

(T+45) + (T + 5) / (T+5)(T+45) = 1/T proceeding further we get

T(T+45) + T(T+5) = (T+5)(T+45) -> T2 + 45T + T2 + 5T = T2 + 45T + 5T + 225

Reducing the equation we get —— T2 = 225 and T = 15.

6. Two workers A & B manufactured a batch of identical parts. A worked for 2 hours and B worked for 3 hours and they did half the job. They worked together for another 3 hours and 1/20 of the job is left out. How much time B would have taken if he had worked alone to complete the job?

Ans: 15 hours

Let ‘x’ and ‘y’ be the time taken by A and B separately to complete the job alone.

We now have an equation —- 2/x + 3/y = 1/2 (job) ——– (i)

After A and B working together for 3 hours the remaining job is —1/20

Thus 19/20 job was already done by A and B individually and jointly.

A and B in 3 hours have completed —- 1 – 1/2 – 1/20 = 9/20 job.

We now have a second equation —- 3/x + 3/y = 9/20 —— (ii)

Solving (i) and (ii) we get the value of ‘y’ as 15 hours.

7. A can do a piece of work in 80 days. He works on it for 10 days and then leave. B then finishes the remaining work in 42 days. If A and B together had worked then in how many days they would have completed the work?

Ans: 30 days.

A in one day can do 1/80 job. So in 10 days he had finished 10/80 -> 1/8 job.

The remaining job was 7/8 and this B completed in 42 days.

So, B in one day can do —- (7/8) / 42 -> 7/ 336 -> 1/48

Thus A and B in one day can do —– 1/80 + 1/48 = (3 + 5)/ 240 -> 8/240 -> 1/30.

Hence A and B together will complete the job in 30 days.

8. 15 men working 8 hours per day take 21 days to complete a work. In how many days 21 women working at 6 hours per day would take to complete the same job if 3 women do as much work as 2 men?

Ans: 30 days.

3 women do as much work as 2 men. So, the 21 women will be equivalent to 14 men.

We can now segment the information as under:

15 M 8 Hours 21 days.

14 M* 6 Hours x days (* relates to 21 women)

X = 21 x 15/14 x 8/6 = 30 days.