Quantitative Aptitude

Time and Work

2,195 Questions
All Pairwise rates and staged schedules 440 Workers-days-hours chain rule 439 LCM units and efficiency ratios 409 Different worker categories 311 Combined rates and an unknown worker 257 Division of wages 219 Alternate work 110 Opposing rates 10

Time and Work Questions

Multiple choice

8 men can finish a piece of work in 21 days. 14 men started working and after 3 days they were replaced by 9 women. These 9 women finished the remaining work in 24 days. In how many days can 9 women finish the whole work?

  1. 32

  2. 31

  3. 30

  4. 29

  5. 28
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total work = 8 * 21 = 168 man-days. 14 men work for 3 days = 42 man-days. Remaining work = 168 - 42 = 126 man-days. 9 women do this in 24 days, so 9 women's efficiency = 126/24 = 5.25 man-days per day. Total work for 9 women = 168 / 5.25 = 32 days.

Multiple choice

Pankaj can produce one unit in 15 days, while Bharti can do the same in 12 days. After producing one unit, working together, they received Rs. 90, which they distributed amongst themselves in proportional to their efficiency. If they work for 20 days, and sell the produce, then Bharti should receive

  1. 150

  2. 160

  3. 170

  4. 180

  5. 190
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Efficiency is inversely proportional to time. Pankaj's rate is 1/15, Bharti's is 1/12. Ratio of efficiencies = (1/15) : (1/12) = 4:5. Total parts = 9. Bharti's share of 90 is (5/9) * 90 = 50 per unit. For 20 days, they produce 20/15 + 20/12 = 4/3 + 5/3 = 3 units. Total earnings = 3 * 90 = 270. Bharti's share = (5/9) * 270 = 150.

Multiple choice

Ram starts working on a job and works on it for 12 days and completes 40% of the work. To help him complete the work, he employs Ravi and together they work for another 12 days and the work gets completed. How much more efficient is Ram than Ravi?

  1. 50%

  2. 75%

  3. 100%

  4. 150%

  5. 200%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ram does 40% in 12 days. Ram's rate = 40/12 = 10/3 % per day. Remaining 60% done by Ram and Ravi in 12 days. Combined rate = 60/12 = 5% per day. Ravi's rate = 5 - 10/3 = 5/3 % per day. Efficiency ratio Ram:Ravi = (10/3) : (5/3) = 2:1. Ram is 100% more efficient than Ravi.

Multiple choice

30 men, working 4 hrs a day can do a piece of work in 10 days. Find the number of days in which 45 men working 8 hrs a day can do twice the work. Assume that 2 men of the first group do as much work in 2 hrs as 4 men of the second group do in 1 hr.

  1. 8(2/3) days

  2. 7(2/3) days

  3. 6(2/3) days

  4. 5(2/3) days

  5. 4(2/3) days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the formula (M1*D1*H1)/W1 = (M2*D2*H2)/W2. The efficiency condition implies 2 men * 2 hrs = 4 men * 1 hr, meaning they have equal efficiency. Thus, (30*10*4)/1 = (45*D2*8)/2. Solving for D2: 1200/1 = 360*D2/2, so 1200 = 180*D2, D2 = 1200/180 = 6.66 or 6(2/3) days.

Multiple choice

A does 75% of a piece of work in 45 days. Then B joins him and they together finish the remaining work in 5 days. How long B alone would take to do the whole work?

  1. 15 days

  2. 45 days

  3. 60 days

  4. 30 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A does 75% in 45 days, so 100% in 60 days. A's rate = 1/60 per day. Remaining work = 25%. A and B finish 25% in 5 days, so their combined rate = 0.25 / 5 = 1/20 per day. B's rate = (1/20) - (1/60) = 3/60 - 1/60 = 2/60 = 1/30. B takes 30 days.

Multiple choice

Zoya alone can complete an assignment in 30 days, and Yasmin alone can complete it in 40 days. If they work together on the assignment for 8 days, what fraction of the work is left?

  1. 5 14

  2. 9 13

  3. 8 15

  4. 7 11

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Combined rate is 1/30 + 1/40 = 7/120 per day. In 8 days they complete 8 x 7/120 = 56/120 = 7/15 of the work, leaving 1 - 7/15 = 8/15. The option '8 15' represents the fraction 8/15 with a missing slash.

Multiple choice

Aman, Simar and Karan can complete an assignment test in 18 days, 21 days and 15 days, respectively. They work together for 4 days. After that, Aman and Simar leave. In how many days will Karan alone complete the remaining test?

  1. 3.2 days

  2. 4 days

  3. 4.8 days

  4. 9.6 days

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work rates: Aman=1/18, Simar=1/21, Karan=1/15. Combined rate = 1/18 + 1/21 + 1/15 = (35+30+42)/630 = 107/630. In 4 days, they do 4 * 107/630 = 428/630. Remaining work = 1 - 428/630 = 202/630. Karan's time = (202/630) / (1/15) = 202/630 * 15 = 202/42 = 4.809 days.

Multiple choice

Sumesh is a mason who can build a hut in 15 days. Ramesh can build the same hut in 25 days. Ramesh works on a new hut for 15 days but then falls sick. He asks Sumesh to complete the remaining work. In how many days can Sumesh complete the remaining work?

  1. 3 days

  2. 6 days

  3. 7 days

  4. 12 days

  5. N/a
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sumesh rate = 1/15 per day. Ramesh rate = 1/25 per day. Ramesh works for 15 days: 15/25 = 3/5 of the work done. Remaining work = 1 - 3/5 = 2/5. Sumesh completes 2/5 work at rate 1/15: (2/5) / (1/15) = (2/5) * 15 = 6 days.

Multiple choice

A and B undertake a piece of work for Rs. 250. A alone can do that work in 5 days and B alone can do that work in 15 days. With the help of C, they finish the work in 3 days. If every one gets paid in proportion to work done by them, what amount will C get?

  1. Rs. 50

  2. Rs. 100

  3. Rs. 150

  4. Rs. 200
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's rate = 1/5, B's rate = 1/15. In 3 days, A does 3/5, B does 3/15 = 1/5. C does 1 - (3/5 + 1/5) = 1/5. Since they are paid in proportion to work, C gets 1/5 of 250 = 50.