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

10 men can complete a work in 7 days. But 10 women need 14 days to complete the same work. How many days will 5 men and 10 women need to complete the work?

  1. 5

  2. 6

  3. 7

  4. 8

  5. 9
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

10 men in 7 days means 1 man does 1/70 of the work per day. 10 women in 14 days means 1 woman does 1/140 of the work per day. 5 men and 10 women do 5/70 + 10/140 = 1/14 + 1/14 = 2/14 = 1/7 of the work per day. They need 7 days to complete the work.

Multiple choice

Kishan takes 24 days to build a building while Neeraj takes 9 days to destroy it completely. If Kishan works for 12 days and then, Neeraj joins him and works for another 6 days only, then in how many days will Kishan alone build the remaining building?

  1. 18 days

  2. 21 days

  3. 22 days

  4. 24 days

  5. 25 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Kishan's rate is 1/24 per day. Neeraj's rate is -1/9 per day. In 12 days, Kishan does 12/24 = 1/2 work. Then they work together for 6 days: 6 * (1/24 - 1/9) = 6 * (3/72 - 8/72) = 6 * (-5/72) = -5/12. Total work done = 1/2 - 5/12 = 1/12. Remaining work = 11/12. Kishan finishes this in (11/12) / (1/24) = 22 days.

Multiple choice

Raju and Dev together can do a piece of work in 10 days. Dev and Sharon can do the same piece of work in 12 days whereas Sharon and Raju can complete it in 15 days. If all the three boys work together, how many days will they take to complete the work?

  1. 4 days

  2. 5 days

  3. 6 days

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

Let R, D, S be rates. R+D = 1/10, D+S = 1/12, S+R = 1/15. 2(R+D+S) = 1/10 + 1/12 + 1/15 = (6+5+4)/60 = 15/60 = 1/4. R+D+S = 1/8. Time = 8 days.

Multiple choice

4 men and 6 women complete a task in 24 days. If the women are at least half as efficient as the men, but not more efficient than the men, what is the range of the number of days for 6 women and 2 men to complete the same task?

  1. 25 to 28 days

  2. 28.1 to 29.9 days

  3. 30 to 33.6 days

  4. 33.7 to 39.9 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let M and W be the efficiency of a man and a woman. 4M + 6W = 1/24. Given 0.5M <= W <= M. For 6W + 2M, we calculate the time T = 1 / (6W + 2M). Substituting the bounds for W, we find the range of T.

Multiple choice

The ratio of working efficiency of Ram and Shyam is 3 : 4. They together can complete a piece of work in 24 days. They started working together & after 6 days Ram leaves and a third person Radha whose efficiency is 6/7 of that of Shyam joins Shyam. Find the time taken by Radha and Shyam together to complete the remaining work.

  1. 221/26

  2. 441/26

  3. cannot be determined

  4. 331/26
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Ram:Shyam efficiency = 3:4. Total work = (3+4)*24 = 168 units. In 6 days, they do 7*6 = 42 units. Remaining = 126. Radha efficiency = 6/7 * 4 = 24/7. Radha + Shyam = 24/7 + 4 = 52/7. Time = 126 / (52/7) = 882/52 = 441/26.

Multiple choice

12 women can complete a project in 36 days and 15 men can complete the same project in 27 days. 16 women start working and after 6 days, they are replaced by 'x' men. If 'x' men can complete the remaining work in 5 days, what is the value of 'x'?

  1. 57

  2. 63

  3. 45

  4. 21

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

12 women * 36 days = 432 man-days. 15 men * 27 days = 405 man-days. 1 woman = 405/432 = 0.9375 men. 16 women work for 6 days = 16 * 0.9375 * 6 = 90 man-days. Remaining work = 405 - 90 = 315 man-days. x men in 5 days = 315 / 5 = 63 men.

Multiple choice

Jack and his brother Mack get a contract to dig a well and on completion, they will get Rs. 36,000. Jack alone can dig a well in 10 days, whereas his brother alone can dig the same well in 5 more days than Jack. They start digging the well with their friend Harry and complete the contract in 5 days. Find the amount (in Rs.) earned by Harry.

  1. 4,000

  2. 6,000

  3. 4,500

  4. 7,500

  5. 4,800
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Jack's rate = 1/10 per day. Mack's rate = 1/15 per day. Together with Harry (H), they finish in 5 days: 5(1/10 + 1/15 + H) = 1. So 1/10 + 1/15 + H = 1/5. H = 1/5 - 1/10 - 1/15 = (6-3-2)/30 = 1/30. Harry's share is (1/30) / (1/5) = 1/6 of the total. 36000 / 6 = 6000.

Multiple choice

Directions : Answer the question independently. Labour allocation is a very important process. A particular weaving section has 20 looms and with five labourers loom efficiency is 75% and production of a loom at 100% efficiency is 10 meter per hour. Salary of a labourer is Rs.11000 per month. I removed one labourer due to which efficiency came down to 70%. How much do I gain or lose due to this action? Assume that profit on one meter cloth is Rs.4 and looms are working for 30 days in a month and 10 hours per day.

  1. Rs.1000 profit

  2. Rs.1500 loss

  3. Rs.1500 profit

  4. Rs.1000 loss
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial production: 20 looms * 10 m/hr * 0.75 efficiency * 300 hrs = 45,000 m. Profit = 45,000 * 4 = 180,000. Costs = 5 * 11,000 = 55,000. Net = 125,000. New production: 20 looms * 10 m/hr * 0.70 efficiency * 300 hrs = 42,000 m. Profit = 42,000 * 4 = 168,000. Costs = 4 * 11,000 = 44,000. Net = 124,000. Loss = 125,000 - 124,000 = 1,000.

Multiple choice

Directions: Answer the question independently. A group of 4 women and 3 men can do a piece of work in 24 days, while a group of 3 women and 4 men can do a piece of work in 25 days. In how many days can a group of 2 women and 4 men can do the same work.

  1. 30

  2. 28

  3. 31

  4. 26
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let W be work of one woman, M be work of one man. 24(4W + 3M) = 25(3W + 4M). 96W + 72M = 75W + 100M. 21W = 28M, so 3W = 4M. Total work = 24(4W + 3(3/4)W) = 24(4W + 2.25W) = 24(6.25W) = 150W. Group of 2W + 4M = 2W + 3W = 5W. Time = 150W / 5W = 30 days.

Multiple choice

Directions: Answer the questions independently of each other. X can do a piece of work in 20 days working 7 hours a day. The work is started by X and on the second day, one man whose capacity to do the work is twice that of X, joined in. On the third day, another man whose capacity is thrice that of X, joined in and this process continued till the work was completed. In how many days will the work be completed, if everyone works for four hours a day?

  1. 5

  2. 6

  3. 7

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

X does 1 unit of work per hour. Total work = 20 * 7 = 140 units. Day 1: X works 4 hours = 4 units. Day 2: X + 2X = 3X works 4 hours = 12 units. Day 3: X + 2X + 3X = 6X works 4 hours = 24 units. Day 4: X + 2X + 3X + 4X = 10X works 4 hours = 40 units. Total so far = 4+12+24+40 = 80 units. Day 5: X + 2X + 3X + 4X + 5X = 15X works 4 hours = 60 units. Total = 140 units. Work completed in 5 days.

Multiple choice

Julie is two times as efficient in stacking crates as Abhijeet and while stacking crates together, they can complete the task in the same time as Rakesh and Amit. If Rakesh and Amit individually take 30 and 20 days, respectively, to complete the task, then how long would it take for just Julie to complete the same task?

  1. 18 days

  2. 32 days

  3. 36 days

  4. 42 days

  5. 46 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rakesh and Amit together: (1/30 + 1/20) = 5/60 = 1/12. So they take 12 days. Julie is 2x efficient as Abhijeet. Let Abhijeet's rate be r, Julie's is 2r. 2r + r = 1/12 => 3r = 1/12 => r = 1/36. Julie's rate = 2r = 2/36 = 1/18. Julie takes 18 days.