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 can do a piece of work in 90 days, B can do it in 40 days and C can do it in 12 days. Each one of them works for a day turn-by-turn. On the first day, A works alone, on the second day, B works alone and on the third day, C works alone. After that, this cycle is repeated till the work is finished. They get Rs. 240 for this job. If the wages are divided in proportion to the work that each has done, then find the amount that each of them will get.

  1. Rs. 14, Rs. 64 and Rs. 162

  2. Rs. 24, Rs. 74 and Rs. 142

  3. Rs. 34, Rs. 64 and Rs. 142

  4. Rs. 24, Rs. 54 and Rs. 162
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A, B, C work rates are 1/90, 1/40, 1/12. In a 3-day cycle, they do (1/90 + 1/40 + 1/12) = (4+9+30)/360 = 43/360. After 8 cycles (24 days), they do 8 * 43/360 = 344/360. Remaining 16/360. Day 25: A does 1/90 = 4/360. Day 26: B does 1/40 = 9/360. Total work: A = 9 * 1/90 + 1/90 = 10/90 = 40/360. B = 8 * 1/40 + 1/40 = 9/40 = 81/360. C = 8 * 1/12 = 8/12 = 240/360. Wages are proportional to work done.

Multiple choice

John works for 5 hours a day for 10 days and completes a piece of work. Bryan works for 8 hours per day for 20 days to complete the same work. Find the ratio of their efficiencies.

  1. 3 : 1

  2. 3 : 2

  3. 2.5 : 1

  4. 3.2 : 1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

John completes the work in 50 hours (5 hours/day * 10 days), and Bryan completes it in 160 hours (8 hours/day * 20 days). Efficiency is inversely proportional to time taken, so the ratio of their efficiencies is 160:50, which simplifies to 3.2:1.

Multiple choice

A group of 25 men and 15 women can do a piece of work in 12 days. The women leave after 8 days and the remaining work is completed by 25 men in 6 days. How many days will 15 women take to do the same work?

  1. 12 days

  2. 36 days

  3. 24 days

  4. 30 days

  5. 35 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total work = (25m + 15w) * 12. Work done in 8 days = (25m + 15w) * 8. Remaining work = (25m + 15w) * 4. This is done by 25m in 6 days: (25m + 15w) * 4 = 25m * 6. Simplifying, 100m + 60w = 150m, so 60w = 50m, or 6w = 5m. Total work = (25 * (6/5)w + 15w) * 12 = 45w * 12 = 540w. 15 women take 540/15 = 36 days.

Multiple choice

Fifteen men could finish a piece of work in 210 days. But at the end of every 10 days, 15 additional men are employed. In how many days will the work be finished?

  1. 60 days

  2. 70 days

  3. 90 days

  4. 100 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total work = 15 * 210 = 3150 man-days. Days 1-10: 15 men * 10 days = 150. Days 11-20: 30 men * 10 days = 300. Days 21-30: 45 men * 10 days = 450. Days 31-40: 60 men * 10 days = 600. Days 41-50: 75 men * 10 days = 750. Days 51-60: 90 men * 10 days = 900. Sum = 150+300+450+600+750+900 = 3150. Work finished in 60 days.