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

A, B and C can individually complete a piece of work in 24 days, 15 days and 12 days respectively. B and C started the work and worked for 3 days and left. The number of days required by A alone to complete the remaining work, is:

  1. 11

  2. 15.5

  3. 18

  4. 66/5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total work = LCM(24, 15, 12) = 120 units. A does 5 units/day, B does 8 units/day, C does 10 units/day. B and C together do 18 units/day for 3 days = 54 units. Remaining work = 120 - 54 = 66 units. A alone needs 66/5 = 13.2 days = 66/5 days.

Multiple choice

$Naimish and Pramod are two friends. A total of Rs. 1800 was paid to both of them for completing a work. Naimish started working and worked for ‘X’ days and then left and the remaining work was completed by Pramod and he was paid Rs. 1080. If Naimish and Pramod alone can complete the work in 30 days and Y days respectively. Which of the following options is /are possible for the value of 'X' and 'Y' are respectively.$ A- 12, 36 B- 12, 30 C- 12, 25 D- 16, 25

  1. Only A

  2. Both B and C

  3. A, B and C

  4. Only C

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

Let Naimish's 1 day work = 1/30. Let Pramod's 1 day work = 1/Y. Naimish worked X days and Pramod completed remaining work. Payment is proportional to work done. Pramod got Rs.1080 out of Rs.1800, so Pramod did 1080/1800 = 3/5 of work. Therefore Naimish did 2/5 of work in X days. X/30 = 2/5 gives X = 12. Pramod completed 3/5 of work alone, so time taken = (3/5)Y. Total work equation: X/30 + (3/5)Y/Y = 1. With X=12: 12/30 + 3/5 = 1, which holds. This works for any Y. Testing options: A (12,36), B (12,30), C (12,25) all satisfy X=12. D (16,25) gives X=16 which doesn't satisfy X/30 = 2/5.

Multiple choice

To complete a certain task, X is 40% more efficient than Y, and Z is 40% less efficient than Y. Working together, they can complete the task in 21 days. Y and Z together worked for 35 days. The remaining work will be completed by X alone in:

  1. 6 days

  2. 8 days

  3. 5 days

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

Let Y's efficiency = 1 unit. X is 40% more efficient (1.4 units) and Z is 40% less efficient (0.6 units). Combined efficiency = 3 units. Total work = 3 × 21 = 63 units. Y + Z work at 1.6 units for 35 days, completing 56 units. Remaining work = 7 units. X at 1.4 units takes 7/1.4 = 5 days. Options A, B, and D are miscalculations.

Multiple choice

Two worker's A and B working together completed a job in (\frac{15}{2}) days. If A worked twice as efficiently as he actually did and B worked thrice as efficiently as he actually did, the work would have been completed in (\frac{10}{3}) days. how many days B require[e to complete the job?

  1. 24 days

  2. 18 days

  3. 36 days

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

Let A and B's actual work rates be 'a' and 'b' jobs per day respectively. Working together: a + b = 1/(15/2) = 2/15. With increased efficiency: 2a + 3b = 1/(10/3) = 3/10. From the first equation: 2a + 2b = 4/15. Subtracting from the second: (2a + 3b) - (2a + 2b) = 3/10 - 4/15, giving b = 9/30 - 8/30 = 1/30. So B alone would take 1/(1/30) = 30 days. Option D is correct. Options A, B, and C don't satisfy the given conditions.

Multiple choice

4 men and 10 women were put on a work. They completed 1/3 of the work in 4 days. After this 2 men and 2 women were increased. They completed 2/9 of the work in 2 days. If the remaining work needs to be completed in 3 days, how many more women need to be increased?

  1. 6

  2. 12

  3. 9

  4. 8
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let one man's work per day be 'm' and one woman's work per day be 'w'. Total work = T. First phase: 4(4m + 10w) = T/3, so 4m + 10w = T/12. Second phase: 2(6m + 12w) = 2T/9, so 6m + 12w = T/9. Solving: From first eq, 12m + 30w = T/3. From second eq, 18m + 36w = T/3. Equating: 12m + 30w = 18m + 36w, so -6m = 6w, or m = -w. This seems wrong. Let me recalculate. Actually: 4 days of (4m+10w) = T/3, so (4m+10w) = T/12. And 2 days of (6m+12w) = 2T/9, so (6m+12w) = T/9. From first: 12m + 30w = T/3. From second: 18m + 36w = T/3. Subtracting: 6m - 6w = 0, so m = w. Then T = 12(4m + 10m) = 12(14m) = 168m, or T = 9(6m + 12m) = 9(18m) = 162m. Hmm, inconsistency. Let me use the second eq: T = 9(6m + 12w) = 54m + 108w. From first eq: 4m + 10w = T/12 = (54m + 108w)/12 = 4.5m + 9w. So 4m + 10w = 4.5m + 9w, giving w = 0.5m. Then T = 54m + 108(0.5m) = 54m + 54m = 108m. Work done so far = T/3 + 2T/9 = 3T/9 + 2T/9 = 5T/9. Remaining = 4T/9 = 4(108m)/9 = 48m. Current team: 6m + 12w = 6m + 12(0.5m) = 6m + 6m = 12m per day. In 3 days: 3 × 12m = 36m. Need 48m - 36m = 12m more. Adding x women: new rate = 12m + xw = 12m + 0.5xm. In 3 days: 3(12m + 0.5xm) = 36m + 1.5xm = 48m. So 1.5xm = 12m, x = 8. Option D is correct.

Multiple choice

In a factory, there are equal number of women and children. Women work for 6 hours a day and children for 4 hours a day. During festival time, the work load goes up by 50\%. The government rule does not allow children to work for more than 6 hours a day. If they are equally efficient and the extra work is done by women, then extra hours of work put in by women every day are

  1. 4

  2. 9

  3. 5

  4. 3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let there be x women and x children. Normally, total work hours = 6x + 4x = 10x. With 50% increase, total work = 15x hours. Children can work max 6 hrs/day (increase of 2x hours). So women must do 15x - 6x = 9x hours. Each woman's increase = 9x - 6x = 3x hours, which is 3 hours per woman.

Multiple choice

A and B together can do a piece of work in 20 days and A alone can do it in 30 days. B alone can do the work in how many days?

  1. 45

  2. 60

  3. 54

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

Use work rates: A+B together complete 1/20 of work per day. A alone does 1/30 per day. So B's rate = 1/20 - 1/30 = 3/60 - 2/60 = 1/60 per day. Therefore B alone needs 60 days. Option A (45) and C (54) are common errors from incorrect arithmetic, while D (30) is A's time.

Multiple choice

Aman and Pramod together can finish a job in 16 days. Pramod can finish the same job on his own in 24 days. How long will Aman alone take to finish that work?

  1. 32

  2. 40

  3. 48

  4. 36
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Aman and Pramod together: 1/16 per day. Pramod alone: 1/24 per day. Aman's rate = 1/16 - 1/24 = 3/48 - 2/48 = 1/48 per day. So Aman needs 48 days alone. Options A (32) and D (36) are arithmetic errors, while B (40) doesn't match the calculation.

Multiple choice

A alone can do a piece of work in 12 days and B alone in 16 days. A, and B undertook to do it for Rs 6400. With the help of C, they completed the work in 6 days. How much is to be paid to C?

  1. 480

  2. 520

  3. 760

  4. 800
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A's work rate = 1/12 per day, B's rate = 1/16 per day. In 6 days, A+B complete 6(1/12 + 1/16) = 6(7/48) = 7/8 of the work. So C does 1/8 of the work in 6 days. Payment is divided by work contribution: C's share = (1/8) × 6400 = Rs 800.

Multiple choice

Aman is four times more efficient than Sangram. Aman can complete a work in 45 days less than Sangram. If both of them work together, then in how many days the work will be completed?

  1. 10

  2. 12

  3. 15

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

Aman is 4 times more efficient than Sangram, so Aman's efficiency: Sangram's efficiency = 4:1. This means if Sangram takes 4x days, Aman takes x days. Given: 4x - x = 45, so 3x = 45, x = 15. Aman takes 15 days, Sangram takes 60 days. Together, their combined rate = 1/15 + 1/60 = 5/60 = 1/12. Working together, they complete the work in 12 days.

Multiple choice

P and Q can do a work in 24 days. Q and R can do the same work in 32 days and R and P can do it in 48 days. Find the approximate time in which P, Q and R can finish the work together.

  1. 11

  2. 8

  3. 23

  4. 21
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let total work = LCM(24,32,48) = 96 units. P+Q = 96/24 = 4 units/day. Q+R = 96/32 = 3 units/day. R+P = 96/48 = 2 units/day. Adding: 2(P+Q+R) = 9, so P+Q+R = 4.5 units/day. Time = 96/4.5 = 21.33 days. Option D (21) is the closest approximation.

Multiple choice

A can finish a work in 20 days and B can finish the same work in 25 days. They began together, but B left the work after 5 days. How many more days will A take to finish the remaining work?

  1. 11

  2. 8

  3. 16

  4. 21
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's work rate = 1/20 per day. B's work rate = 1/25 per day. Combined rate = 1/20 + 1/25 = 9/100 per day. In 5 days together, they complete 5 × 9/100 = 45/100 = 9/20 of the work. Remaining work = 11/20. A alone needs (11/20) ÷ (1/20) = 11 more days to finish.