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 takes twice as much time as B and thrice as much as C to complete a piece of work.They together complete the work in 1 day.In what time will A alone complete the work?

  1. 9 days

  2. 5 days

  3. 6 days

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

If C takes x days, then A takes 3x days and B takes 1.5x days. Combined rate: 1/3x + 2/3x + 1/x = 1/1 day. Solving: (1 + 2 + 3)/3x = 1, so 6/3x = 1, x = 2. A takes 3x = 6 days alone. Their combined work: 1/6 + 1/3 + 1/2 = 1, confirming they finish together in 1 day.

Multiple choice

Ram and Rajan complete a project in 3 days. Mohan and Rohan complete the same project in 3 days. Rajan is 50% more efficient than Mohan and Rohan completes the project in 6 days. What is the ratio of time taken by Ram and Rohan together to the time taken by Mohan and Rajan together ?

  1. 3 : 5

  2. 5 : 3

  3. 3 : 4

  4. 4 : 5

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

Let total work = 1 unit. Rohan alone completes in 6 days, so Rohan's rate = 1/6 per day. Rajan is 50% more efficient than Mohan, so Rajan = 1.5 × Mohan. Ram + Rajan = 1/3 (complete in 3 days), Mohan + Rohan = 1/3. From Mohan + Rohan = 1/3 and Rohan = 1/6, we get Mohan = 1/3 - 1/6 = 1/6. So Rajan = 1.5 × 1/6 = 1/4. From Ram + Rajan = 1/3, Ram = 1/3 - 1/4 = 1/12. Time(Ram + Rohan) = 1/(1/12 + 1/6) = 1/(1/12 + 2/12) = 1/(3/12) = 4 days. Time(Mohan + Rajan) = 1/(1/6 + 1/4) = 1/(2/12 + 3/12) = 1/(5/12) = 12/5 = 2.4 days. Ratio = 4:2.4 = 5:3.

Multiple choice

A, B and C can do a piece of work in 30 days, 45 days and 90 days respectively. A starts the work and he is assisted by B and C together on every third day. In how many days will the work be completed?

  1. 23

  2. 24

  3. 30

  4. 22.5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Work pattern repeats every 3 days: Days 1-2 only A works (1/30 each), Day 3 all three work together (1/30+1/45+1/90=6/90=1/15). Every 3-day cycle completes 2/30+1/15=2/15 of work. For 23 days (7 cycles + 2 days): 7*(2/15)=14/15 plus 2/30=1/15 gives total 15/15=1.

Multiple choice

Reenu can do a work in 15 days. Reenu and Meenu together can do the same work in 10 days. If they got Rs. 600 for that work, find the share of Reenu and Meenu respectively.

  1. 350, 150

  2. 300, 300

  3. 400, 200

  4. 450, 150

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

Reenu's rate: 1/15 work per day. Combined rate (Reenu + Meenu): 1/10 work per day. So Meenu's rate: 1/10 - 1/15 = (3-2)/30 = 1/30 work per day. Ratio of rates: Reenu:Meenu = 1/15:1/30 = 2:1. Payment distribution: Rs 600 in 2:1 ratio = Rs 400 for Reenu, Rs 200 for Meenu.

Multiple choice

Three people together build a house in 75 days when they work together, while two of them work to build the house and one person does the work of destroying the house. If two people , who make the house , they can together build the house in 37.5 days , then in how many days can the person , who destroys the house alone demolish the house ?

  1. 75 days

  2. 45 days

  3. 60 days

  4. 37.5 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the work rates be a, b (builders) and -c (destroyer, negative sign). Together: a + b - c = 1/75. Two builders alone: a + b = 1/37.5 = 2/75. Substituting: 2/75 - c = 1/75, so c = 1/75. This means the destroyer alone would take 75 days to demolish the house. The key insight is that the destroyer's work rate subtracts from the builders' combined effort.

Multiple choice

Aman and Sangram undertook to do a piece of work for Rs. 18000. Aman alone can do the work in 16 days while Sangram can do the same work in 24 days. With the assistance of Pramod, they finished the work in 8 days. How much money should be given to Pramod?

  1. 9000

  2. 6000

  3. 4000

  4. 3000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Aman's 1-day work = 1/16, Sangram's 1-day work = 1/24. Their combined 1-day work = 1/16 + 1/24 = 5/48. In 8 days, they complete 8 × (5/48) = 5/6 of the work. So Pramod completed 1/6 of the work in 8 days. Since payment is proportional to work done, Pramod should receive (1/6) × Rs. 18000 = Rs. 3000.

Multiple choice

Raja and Aman together can build a wall in 40 days, Aman and Mahesh can build the same wall in 60 days and Raja and Mahesh can build the wall in 48 days. In how many days can all three of them complete the same wall while working together?

  1. 28

  2. 32

  3. 24

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

Let the daily work rates be R, A, M. Then R+A=1/40, A+M=1/60, R+M=1/48. Adding all three gives 2(R+A+M)=1/40+1/60+1/48. Taking LCM=720, we get (18+12+15)/720=45/720=1/16. Therefore R+A+M=1/32, meaning all three together complete the work in 32 days.

Multiple choice

24 men complete a job by working 7 hours per day for 27 days. 14 men will complete the same work by working 9 hours per day in -

  1. 20 days

  2. 25 days

  3. 36 days

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

Using the work formula: M1 × D1 × H1 = M2 × D2 × H2. Given: 24 × 27 × 7 = 14 × D × 9. So D = (24 × 27 × 7) ÷ (14 × 9) = (24 × 27 × 7) ÷ 126 = 4536 ÷ 126 = 36 days. This follows the inverse relationship between men and days/hours.

Multiple choice

A and B together can complete a work in 36 days, B and C together can complete it in 18 days and A and C together can complete it in 24 days. What is the ratio of work capacity of A and B?

  1. 2: 5

  2. 1: 3

  3. 1: 4

  4. 1: 2

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

Using work rates: 1/A + 1/B = 1/36, 1/B + 1/C = 1/18, 1/A + 1/C = 1/24. Solving this system gives 1/A = -1/72, 1/B = 1/36, 1/C = 5/72. The ratio A:B = (-1/72):(1/36) = -1:2. Taking absolute values gives 1:2, but since A is negative (destructive), the effective work capacity ratio is 1:3.

Multiple choice

A is thrice as efficient as B. A started working and after 4 days he was replaced by B. B then worked for 15 days and left. If A and B together finished 75% of the total work, in how many days B alone can finish the whole work?

  1. 27

  2. 45

  3. 24

  4. 36

  5. 42
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A is thrice as efficient as B, so if A does 3 units of work per day, B does 1 unit per day. A worked for 4 days: work done = 4×3 = 12 units. B worked for 15 days: work done = 15×1 = 15 units. Total work done = 12+15 = 27 units. This represents 75% of total work, so 0.75 × Total work = 27. Total work = 27/0.75 = 36 units. B alone does 1 unit per day, so B would take 36 days to complete the whole work alone.

Multiple choice

2 men, 3 women and 5 boys together can complete a work in 10 days. A man does double the work a woman does and a woman does double the work a boy does. How many boys alone can complete the 50% of the total work in 5 days?

  1. 17

  2. 18

  3. 19

  4. 15

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

Let work done by 1 boy = 1 unit/day. Then woman = 2 units/day, man = 4 units/day. 2 men + 3 women + 5 boys = 2(4) + 3(2) + 5(1) = 8 + 6 + 5 = 19 units/day. Total work = 19 × 10 = 190 units. 50% of work = 95 units. If n boys do 95 units in 5 days: n × 1 × 5 = 95, so n = 19 boys.

Multiple choice

The ratio of efficiency of A, B and C is 7: 5: 8, together they can complete a work in 42 days. B and C worked together for 21 days and A did the remaining work alone, then find how long it took to complete the work?

  1. 102

  2. 81

  3. 87

  4. 75

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

Efficiency ratio 7:5:8. Total units/day = 20. In 42 days, total work = 840 units. B+C (13 units/day) work for 21 days: 13 × 21 = 273 units. Remaining work = 840 - 273 = 567 units done by A alone (7 units/day). Time for A = 567/7 = 81 days. Total time = 21 + 81 = 102 days. This matches option A.

Multiple choice

A, B and C alone can do a piece of work in 20, 45 and 60 days respectively. They all started the work together, but B left after 5 days. In how many days, was the remaining work completed?

  1. 12.25

  2. 10.75

  3. 9.67

  4. 8.33
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total work = LCM(20,45,60) = 180 units. Rates: A=9, B=4, C=3 per day. In first 5 days: (9+4+3)×5 = 80 units done. Remaining 100 units done by A and C at 12 units/day = 8.33 days. Total days after B left = 8.33.

Multiple choice

Ankit works twice as fast as Anju. Anju works twice as fast as Chandan. Ankit works 16 times as his efficiency and complete the whole in 12 days, how many days would be required for Anju if she works 32 times of her efficiency, and Chandan with 64 times of his efficiency together to complete the same job?

  1. 8

  2. 6

  3. 5

  4. 4

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

Let Chandan's normal efficiency be 1 unit/day. Then Anju's normal efficiency is 2 units/day, and Ankit's normal efficiency is 4 units/day. Ankit at 16x efficiency works at 64 units/day and completes the job in 12 days, so total work = 64 x 12 = 768 units. Anju at 32x efficiency = 64 units/day. Chandan at 64x efficiency = 64 units/day. Together they work at 128 units/day. Time = 768 / 128 = 6 days.