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

The time taken by 4 men to complete a job is double the time taken by 5 children to complete the same job. Each man is twice as fast as a woman. How long will 12 men, 10 children and 8 women take to complete a job, given that a child would finish the job in 20 days?

  1. 4 days

  2. 3 days

  3. 2 days

  4. 1 day
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A child finishes in 20 days, so 1 child's rate is 1/20. 5 children take 4 days, so 4 men take 8 days (double time), meaning 1 man's rate is 1/32. Since 1 man is twice as fast as a woman, 1 woman's rate is 1/64. Total rate for 12 men, 10 children, 8 women = 12/32 + 10/20 + 8/64 = 3/8 + 1/2 + 1/8 = 1. The job takes 1/1 = 1 day.

Multiple choice

Three engineers A, B and C take up an assignment from a company. A and B together can complete this assignment in 6 days, B and C together can complete it in 12 days, while A and C together can complete it in 3 days. What will be the number of days taken by C to complete the assignment working alone?

  1. 3

  2. 4

  3. 6

  4. 8

  5. 10
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A+B = 1/6, B+C = 1/12, A+C = 1/3. Summing these: 2(A+B+C) = 1/6 + 1/12 + 4/12 = 7/12. A+B+C = 7/24. C = (A+B+C) - (A+B) = 7/24 - 4/24 = 3/24 = 1/8. So C takes 8 days.

Multiple choice

A and B together can complete a task in 40 days. B and C together can complete the same task in 50 days. A and C together can complete the same task in 60 days. What is the respective ratio between the numbers of days taken by A and C while completing the same task alone?

  1. 7 : 13

  2. 13 : 7

  3. 7 : 12

  4. 12 : 7

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

1/A + 1/B = 1/40, 1/B + 1/C = 1/50, 1/A + 1/C = 1/60. Adding these: 2(1/A + 1/B + 1/C) = 1/40 + 1/50 + 1/60 = (15+12+10)/600 = 37/600. So 1/A + 1/B + 1/C = 37/1200. 1/C = 37/1200 - 1/40 = 7/1200. 1/A = 37/1200 - 1/50 = 13/1200. Ratio A:C = 1200/13 : 1200/7 = 7:13.

Multiple choice

Vibhu alone can do a certain task in 24 days and Kashish alone can do the same task in 48 days. They start the task together and then due to some reason, Vibhu leaves 12 days before the task is completed. In total how many days is the task completed?

  1. 26 days

  2. 24 days

  3. 23 days

  4. 22 days.

  5. 20 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Vibhu does 1/24 per day, Kashish does 1/48 per day. Together they do 3/48 = 1/16 per day. Let total days be x. Kashish works for x days, Vibhu works for x-12 days. (x-12)/24 + x/48 = 1. Multiply by 48: 2(x-12) + x = 48. 2x - 24 + x = 48. 3x = 72. x = 24.

Multiple choice

A and B together can do a piece of work in 80 days. B and C can do it in 120 days. On the first day, only A and B worked together and on the second day, only B and C worked together. For the following days, B worked for all the days, but A and C worked on alternate days only. How long did the work last?

  1. 88 days

  2. 90 days

  3. 96 days

  4. 98 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A+B = 1/80, B+C = 1/120. Let B's rate be b. A = 1/80 - b, C = 1/120 - b. Day 1: A+B = 1/80. Day 2: B+C = 1/120. Day 3: A+B = 1/80. Day 4: B+C = 1/120. In 2 days, work done = 1/80 + 1/120 = 5/240 = 1/48. Total work = 1. Days = 1 / (1/96) = 96 days.

Multiple choice

A alone can do a piece of work in 14 days, which B alone can do in 21 days. They work together for 7 days, after which A quits. B is now joined by another person C, who does half as much work as A in a day. How many days will it take for B and C to complete the remaining work, after A quits?

  1. 4 days

  2. 3 days

  3. 2 days

  4. 1 day

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

A's rate = 1/14, B's rate = 1/21. Together = 1/14 + 1/21 = 3/42 + 2/42 = 5/42. In 7 days, they do 7 * 5/42 = 5/6 of the work. Remaining = 1/6. C's rate = 1/2 * A's rate = 1/28. B+C rate = 1/21 + 1/28 = 4/84 + 3/84 = 7/84 = 1/12. Time to finish 1/6 work = (1/6) / (1/12) = 2 days.

Multiple choice

Eight boys and 12 girls can complete a piece of work in 8 days, and 14 girls with 6 boys can do the same work in 10 days. Find the time taken by 20 girls to complete the work.

  1. 12 days

  2. 40 days

  3. 6 days

  4. 9 days

  5. 16 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let B be the work of a boy per day and G be the work of a girl per day. 8B + 12G = 1/8 and 6B + 14G = 1/10. Solving this system: multiply first by 3 and second by 4: 24B + 36G = 3/8 and 24B + 56G = 4/10. Subtracting gives 20G = 4/10 - 3/8 = 16/40 - 15/40 = 1/40. Thus, 20 girls complete the work in 40 days.

Multiple choice

A team leader undertook a certain project to complete in 44 days. He used 21 team members to complete the task. But after 11th day, only 1/6th work was completed. How many extra members will be required to complete the work in the stipulated time?

  1. 20

  2. 17

  3. 19

  4. 14

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

In the first 11 days, 21 members completed 1/6 of the work. To find the total number of members (M) needed to complete the remaining 5/6 of the work in the remaining 33 days, we use the work formula: (21 * 11) / (1/6) = (M * 33) / (5/6). Solving this gives M = 35 members, which means 35 - 21 = 14 extra members are required.