Time and Work Aptitude Questions

Q1. A can do (1/3) of a work in 5 days and B can do (2/5) of the work in 10 days. In how many days both A and B together can do the work?

1/3 of work is done by A in 5 days

Therefore, whole work will be done by A in 15 days

2/5 of work is done by B in 10 days

Whole work will be done by B in (10 x 5/2) i.e.., 25 days

Therefore (A + B)’s 1 day’s work = (1/15 + 1/25) = 8/75

So both together can finish 75/8 days i.e.., 9 3/8 days

Q2. A, B and C contract a work for Rs. 550. Together A and B are to do 7/11 of the work. The share of C should be?

Work to be done by C = (1 – 7/11) = 4/11

Therefore, (A +B) = C = 7/11 : 4/11 = 7 : 4

Therefore C’s share = Rs.(550 x 4/11) = Rs. 200

Q3. A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the work in 42 days. The Two together could complete the work in?

A’s 10 days work = (10 x 1/80) = 1/8

Remaining work = (1 -1/8) = 7/8

Therefore 7/8 work is done by A in 42 days.

Whole work will be done by A in (42 x 8/7)i.e.., 48 days

Therefore, (A+ B)’s 1 day work = (1/80 + 1/48) = 8/240 = 1/30.

A and B together can finish it in 30days.

Q4. Mahesh and Umesh can complete a work in 10 days and 15 days respectively. Umesh starts the work and after 5 days Mahesh also joins him in all the work would be completed in

Umesh’s 5 day’s work = 5 x 1/15 = 1/3

Remaining work = (1 – 1/3) = 2/3 (1/10 +1/ 15) work is done by both in 1 day

Therefore 2/3 work is done by both in (6 x 2/3) = 4days.

The work was completed in 9 days

Q5. Twelve men can complete a work in 8 days. Three days after they started the work, 3 more men joined them. In how many days will all of them together complete remaining work?

1 man’s one day’s work = 1/96 12 men’s 3 day’s work = (3 x 1/8) = 3/8

Remaining work = (1 – 3/8) = 5/8 15 men’s 1 day’s work = 15/96

Now 15/96 work is done by them in 1day

Therefore 5/8 work will be done by them in (96/15 x 5/8) i.e., 4 days

Q6. A can do a piece of work in 10 days and B can do the same piece of work in 20 days. They start the work together but after 5 days. A leaves off B will do the remaining piece of work in?

(A +B)’s 5 days work = 5 (1/10 +1/20) = ¾

Remaining work =(1 -3/4) = ¼ 1/20work is done by B in 1 day.

Therefore, ¼ work is done by B in (20 x 1/4)i.e.., 5 days

Q7. A and B can together finish a work in 30 days. They worked for it for 20 days and then B left. The remaining work was done by A alone in 20 more days. Alone can finish the work in?

(A+ B)’s 20 day’s work =(20 x 1/30) = 2/3

Remaining work = (1 -2/3) = 1/3 1/3 work is done by A in 20 days

Whole work can be done by A in (3 x 20)days i.e.., 60 days

Q8. A can complete a job in 9 days. B in 10 days and C in 15 days. B and C start the work and are forced to leave after 2 days. The time taken to complete the remaining work is?

(B + C)’s 2 day’s work = 2 (1/10 + 1/15) = 1/3 Remaining work = (1 – 1/3) = 2/3 1/9 work is done by A in 1 day Therefore 2/3 work is done by A in (9 x 2/3) = 6 days

Q9. A, B and C together earn Rs.150 per day while A and C together earn Rs. 94 and B and C together earn Rs. 76. The daily earning of C is?

B’s daily earning = RS.(150 -94) = Rs. 56

A’s daily earning = Rs.(150 -76) = Rs.74

C’s daily earning = Rs.[150 – (56+74)] = Rs. 20

Q10. A can do a certain job in 12 days. B is 60% more efficient than A. Then Number of days it takes B to do the same piece of work is?

Ratio of times taken by A and B = 160 : 100 = 8 : 5

If A takes 8 days B takes 5 days

If A takes 12 days, B takes =(5/8 x 12) = 7 ½ days