Time & Work Aptitude Questions with Solutions
44 Time & Work questions with hints, worked solutions and time targets — 7 easy · 22 medium · 15 hard.
- Section: Quantitative Aptitude
- Questions: 44
- By difficulty: 7 easy · 22 medium · 15 hard
- Cost: Free, unlimited on every plan
Rates of work, pipes and cisterns, alternating days and efficiency.
Time & Work: the essentials
- Work in rates, not times: a job done in a days is 1/a of the job per day. Rates add; times do not.
- A in a days and B in b days, working together: ab/(a + b) days.
- LCM method: take the total work as the LCM of the given times, so every rate is a whole number of units a day.
- Efficiency is inversely proportional to time. Twice as efficient means half the time; x% more efficient means 100x/(100 + x) per cent less time.
- Three pairs: adding the rates of A + B, B + C and C + A counts everyone twice, so halve the sum.
- Chain rule: (M₁ × D₁ × H₁)/W₁ = (M₂ × D₂ × H₂)/W₂ for men, days, hours and work done. Convert a mixed gang of men and women into one unit first.
- Pipes and cisterns: inlets add rate, outlets and leaks subtract it. A pipe that fills in a hours but takes b hours with a leak means the leak alone empties it in ab/(b − a) hours.
- Alternate days: find the work per cycle, count the whole cycles, then finish the remainder day by day, in order.
- When someone leaves early, write one equation in the total time; the leaver works fewer days.
Example: A takes 24 days and B 40. Take the job as 120 units: A does 5 a day and B 3, so together they need 120/8 = 15 days.
Questions
- A and B working together Easy
A can finish a job in 12 days and B in 18 days. Working together, how long do they take? - A leaves after four days Medium
A and B can finish a job in 10 and 15 days respectively. They start together, but A leaves after 4 days. How many more days does B need to finish? - Two inlets and one outlet Medium
Pipe A fills a tank in 6 hours, pipe B in 9 hours, and pipe C empties a full tank in 18 hours. With all three open, how long does the tank take to fill? - A is twice as efficient as B Medium
A is twice as efficient as B, and together they finish a job in 8 days. How long would B alone take? - Men, women and one job Medium
6 men or 10 women can complete a job in 15 days. How many days will 3 men and 5 women take together? - Working on alternate days Hard
A can do a job in 10 days and B in 15 days. They work on alternate days, A starting first. In how many days is the job finished? - A in 10 days, B in 15 Easy
A can finish a job in 10 days and B in 15 days. Working together, how long do they take? - A in 6 days, B in 10 Easy
A can do a piece of work in 6 days and B in 10 days. How long will they take together? - Finding B's time alone Easy
A and B together can complete a work in 8 days. A alone takes 12 days. How long would B alone take? - Twice as fast Medium
A works twice as fast as B. Together they finish a job in 12 days. How long would B alone take? - Three times as good, sixty days sooner Hard
A is three times as good a workman as B and takes 60 days less than B to finish a job. How long do they take working together? - Twenty-five percent more efficient Hard
A is 25% more efficient than B and takes 10 days less to finish a job. How many days does A take? - Finding C's time Medium
A, B and C together finish a work in 4 days. A alone takes 12 days and B alone 18 days. How long would C alone take? - Three pairs of workers Hard
A and B together can do a work in 12 days, B and C in 15 days, and C and A in 20 days. How long will all three together take? - A alone, from the pairs Medium
A and B together take 12 days, B and C take 15 days, and all three together take 10 days. How long would A alone take? - A starts, B finishes Medium
A can do a work in 15 days. He works for 5 days and then B finishes the rest in 12 days. How long would B alone take for the whole work? - Together, then B alone Medium
A can do a work in 12 days and B in 15 days. They work together for 4 days, after which A leaves. In how many more days will B finish? - B leaves partway Medium
A and B together can do a work in 30 days. They work together for 20 days, then B leaves and A finishes the rest in 20 more days. - A leaves five days before the end Hard
A can do a work in 20 days and B in 30 days. They begin together, but A leaves 5 days before the work is finished. In how many days is the work completed? - Alternate days: 20 and 30 days Hard
A can complete a work in 20 days and B in 30 days. They work on alternate days, with A starting. In how many days is the work finished? - Two taps used alternately Hard
Tap A fills a tank in 4 hours and tap B in 6 hours. They are opened alternately for one hour each, starting with A. How long does the tank take to fill? - Two inlets and an outlet Medium
Pipe A fills a tank in 12 hours, pipe B in 15 hours, and pipe C empties a full tank in 20 hours. With all three open, how long does the tank take to fill? - A leak in the tank Easy
A tap fills a tank in 6 hours. A leak at the bottom empties a full tank in 12 hours. With both working, how long does the tank take to fill? - The leak costs an hour Medium
A pipe fills a cistern in 4 hours, but because of a leak it takes 1 hour longer. How long would the leak alone take to empty a full cistern? - From nine hours to ten Medium
A cistern is normally filled in 9 hours, but a leak makes it take 10 hours. How long would the leak alone take to empty the full cistern? - Closing one tap early Hard
Two pipes fill a tank in 20 minutes and 30 minutes respectively. - One pipe finishes the job Medium
Two pipes can fill a tank in 10 minutes and 15 minutes. Both are opened for 4 minutes, then the first is closed. - Capacity from a waste pipe Hard
Two taps fill a cistern in 30 and 40 minutes. A waste pipe empties 3 gallons per minute. With all three open the cistern fills in 60 minutes. - Men and women together Medium
3 men or 6 women can complete a work in 20 days. How long will 4 men and 4 women take? - Women and children Medium
10 women can complete a work in 7 days and 10 children take 14 days. How long will 5 women and 10 children take together? - More men to finish in 6 days instead of 8 Easy
12 men can complete a work in 8 days. How many men are needed to finish it in 6 days? - More men join partway Hard
12 men undertake a work expected to take 20 days. After 8 days, 4 more men join. In how many days in total is the work finished? - Some men leave Medium
24 men can complete a work in 16 days. After 4 days, 8 men leave. How many more days will the rest take to finish? - A contractor falls behind Hard
A contractor undertakes to finish a job in 40 days with 100 men. After 30 days only two-thirds of the work is done. - Hectares reaped Medium
If 8 men can reap 80 hectares in 24 days, how many hectares can 36 men reap in 30 days? - Length of wall built Medium
If 20 men can build a wall 56 metres long in 6 days, what length can 35 men build in 3 days? - Working different hours a day Medium
39 people can repair a road in 12 days working 5 hours a day. In how many days will 30 people working 6 hours a day complete it? - Men, women and hours Hard
15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take, if 3 women do as much work as 2 men? - Half the work, a third of the work Medium
A does half a job in 5 days; B does one-third of the same job in 5 days. How long will they take together to complete it? - Four-fifths done in twenty days Easy
A completes four-fifths of a work in 20 days. How many more days will he take to finish the rest? - Sharing the payment Hard
A can do a work in 6 days and B in 8 days. With C's help they finish it in 3 days and are paid ₹600 in all. What is C's share? - C's help finishes it in four days Medium
A alone takes 8 days and B alone 12 days. With C's help they finish the work in 4 days. How long would C alone take? - Capacity from a tap and a leak Hard
A leak can empty a full tank in 8 hours. With a tap admitting 6 litres per minute also open, the full tank empties in 12 hours. - How long B alone would take Hard
A and B can do a work in 10 days, B and C in 15 days, and A and C in 12 days. How long would B alone take?
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