Quantitative Aptitude

Time and Work

2,195 Questions
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Time and Work Questions

Multiple choice

Directions: You are given two quantities, Quantity I and Quantity II. Compare the two quantities and choose the correct option accordingly. A can finish a work in 24 days, B in 9 days and C in 12 days. They work together for 3 days. Quantity I. Time taken by A and C to do the remaining work Quantity II. Time taken by B and C to do the remaining work

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I = Quantity II

  4. No relation
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A=1/24, B=1/9, C=1/12. Combined rate = 1/24 + 1/9 + 1/12 = (3+8+6)/72 = 17/72. In 3 days, they do 3 * 17/72 = 17/24. Remaining = 7/24. Q1: Time for A and C = (7/24) / (1/24 + 1/12) = (7/24) / (3/24) = 7/3 = 2.33 days. Q2: Time for B and C = (7/24) / (1/9 + 1/12) = (7/24) / (7/36) = (7/24) * (36/7) = 1.5 days. Q1 > Q2.

Multiple choice

5 men finish a work in 24 days, working 6 hours a day; while 10 women finish the same work, working 8 hours a day. Given that 2 men work as much as 3 women, the number of days in which the women finish the work is

  1. 10 ¼

  2. 12

  3. 13 ½

  4. 15

  5. 15 ¾
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work = 5 men * 24 days * 6 hours = 720 man-hours. 2 men = 3 women, so 1 man = 1.5 women. 5 men = 7.5 women. 7.5 women * 24 days * 6 hours = 1080 woman-hours. Women work 8 hours/day. Days = 1080 / (10 women * 8 hours) = 1080 / 80 = 13.5 days.

Multiple choice

A and B together can dig a pond in 10 days. They worked together for 4 days and then B left the job. In how many days would A complete the job, if he can alone dig the pond in 30 days?

  1. 12 days

  2. 14 days

  3. 18 days

  4. 30 days

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

A's rate = 1/30. (A+B)'s rate = 1/10. So B's rate = 1/10 - 1/30 = 2/30 = 1/15. They work together for 4 days: 4 * (1/10) = 4/10 = 2/5. Remaining work = 3/5. A completes this in (3/5) / (1/30) = 3/5 * 30 = 18 days.

Multiple choice

X takes 15 days to do a job. He works on it for 3 days and then, Y alone finishes the remaining job in 8 days. In how much time will X and Y finish the job, if they work together?

  1. 4 days

  2. 6 days

  3. 30 days

  4. 10 days

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

X does 1/15 of the job per day. In 3 days, X does 3/15 = 1/5 of the job. Remaining job is 4/5, which Y finishes in 8 days, so Y's rate is (4/5) / 8 = 1/10 per day. Combined rate is 1/15 + 1/10 = 5/30 = 1/6, so they take 6 days together.

Multiple choice

Renu alone can do a piece of work in 8 days and Suhavi alone can do it in 10 days. If Seema joins them, they finish the work in 4 days. Find the share of Renu, if the trio undertakes to finish the work for a remuneration of Rs. 800.

  1. Rs. 320

  2. Rs. 400

  3. Rs. 200

  4. Rs. 550

  5. Rs. 620
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Renu's rate is 1/8, Suhavi's is 1/10. Together with Seema, the rate is 1/4. Seema's rate = 1/4 - (1/8 + 1/10) = 1/4 - 9/40 = 1/40. The work shares are proportional to rates: Renu 1/8, Suhavi 1/10, Seema 1/40. Ratio is 5:4:1. Renu's share = (5/10)*800 = 400.

Multiple choice

Amit and Sujit together can complete an assignment of data entry in five days. Sujit's speed is 80% of Amit's speed and the total key depressions in the assignment are 5,76,000. What is Amit's speed in key depressions per hour if they work for 8 hours a day?

  1. 4,800

  2. 6,400

  3. 8,000

  4. 7,200

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

Total work = 5,76,000. Combined rate = 5,76,000 / (5 days * 8 hours) = 14,400 per hour. Let Amit's speed be A. Sujit's speed = 0.8A. A + 0.8A = 14,400, so 1.8A = 14,400. A = 14,400 / 1.8 = 8,000.

Multiple choice

A can do a piece of work in 10 days and B can do the same work in 15 days. A and B start a work together. A works at 1/3rd of his usual efficiency and B works at half of his usual efficiency. How many days will they take to complete a piece of work which is twice as large as the original work?

  1. 15

  2. 30

  3. 12

  4. 10

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

A's usual rate = 1/10, B's = 1/15. New rates: A = 1/30, B = 1/30. Combined rate = 2/30 = 1/15. To do twice the work (2 units), time = 2 / (1/15) = 30 days.

Multiple choice

Ram takes twice the time taken by Shyam and thrice the time taken by Laxman to do a particular work. Working together, they can complete the work in 2 days. Find the respective number of days taken by A, B and C to complete the work alone.

  1. 12, 6, 4

  2. 18, 9, 6

  3. 24, 12, 8

  4. 30, 15, 10

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

The times taken by Ram, Shyam, and Laxman are in the ratio 6:3:2. Their combined rate is therefore 1/6 + 1/3 + 1/2 = 1/2 work per day, so their individual times are 12, 6, and 4 days. The question switches from the names Ram, Shyam, and Laxman to A, B, and C.

Multiple choice

Raju and Kamal decided to do a given task together but by doing it on alternate days. Raju alone could do the task in 15 days and Kamal alone could do the task in 20 days. When they started working together alternately, Raju said that he would start from the first day. In how many days would the task get finished?

  1. 11

  2. 13

  3. 15

  4. 17

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

Raju's rate = 1/15, Kamal's rate = 1/20. In a 2-day cycle, they do 1/15 + 1/20 = 7/60 of the work. In 8 cycles (16 days), they do 8 * (7/60) = 56/60. Remaining work = 4/60 = 1/15. On day 17, Raju works and completes 1/15. Total = 17 days.