Quantitative Techniques · Micro-test

Time and Work

Every time and work question turns on one idea: a person who finishes a job in n days does one-nth of it each day. Add the daily fractions and the rest is arithmetic.

10 questions · 5 minutes · instant scoring

What this topic actually tests

If A finishes a job in 12 days, A's rate is 1/12 of the job a day. If B's rate is 1/18, together they do 1/12 + 1/18 = 5/36 of the job a day and finish in 36/5 days, that is 7 1/5 days. For two workers the shortcut is product over sum: (12 × 18) ÷ (12 + 18) = 7.2. When the combined time is given and one worker's time is known, subtract the rates: together in 6 days and A alone in 10 means B's rate is 1/6 − 1/10 = 1/15. When someone leaves partway, work out the fraction done up to that point, subtract from 1, and divide what remains by the rate of whoever is left. Efficiency is rate: 'A is twice as efficient as B' means A's daily fraction is twice B's, and A takes half the time. Pipes are the same problem, with a leak or an emptying pipe counted as a negative rate. Questions about numbers of workers use total effort, which stays fixed: workers × days (and × hours a day, if given) is the same before and after. Wages for a job done together are shared in proportion to the work each did, which, when both work the same number of days, is the ratio of their rates. Worked example: 12 workers take 15 days, so the job is 180 worker-days, and 20 workers take 180 ÷ 20 = 9 days.

The common trap on this topic

The classic error is adding the times instead of the rates: 12 days and 18 days do not make 30 days, or 15. Two people working together must take less time than the faster of them alone, so an answer greater than 12 is impossible here and can be struck out at once. The second error is in wage questions, where the money is divided in the ratio of the times instead of the ratio of the work done; the faster worker, who has the smaller time, earns more. The third is forgetting, in a leak question, that the leak's rate is subtracted, which makes the tank take longer, never less.

Time and Work: answers and explanations

A can finish a piece of work in 12 days and B can finish it in 18 days. Working together, in how many days will they finish it?
Answer: C. 7 1/5 days
Their daily rates add: 1/12 + 1/18 = 3/36 + 2/36 = 5/36. The time is 36/5 = 7 1/5 days. Fifteen is the average of the two times, which cannot be right, since together they must be quicker than A alone.
A and B together can finish a job in 6 days. A alone can finish it in 10 days. In how many days can B alone finish it?
Answer: C. 15 days
B's rate is 1/6 − 1/10 = 5/30 − 3/30 = 2/30 = 1/15, so B alone takes 15 days.
12 workers can complete a job in 15 days. In how many days can 20 workers of the same efficiency complete it?
Answer: A. 9 days
The job is 12 × 15 = 180 worker-days. With 20 workers it takes 180 ÷ 20 = 9 days.
A is twice as efficient as B. Working together they finish a job in 8 days. In how many days can B alone finish it?
Answer: C. 24 days
If B does 1 unit a day, A does 2, and together they do 3. In 8 days they do 24 units, which is the whole job. B alone, at 1 unit a day, takes 24 days; A alone would take 12.
Pipe A can fill a tank in 20 minutes and pipe B can fill it in 30 minutes. If both are opened together, how long will the tank take to fill?
Answer: A. 12 minutes
1/20 + 1/30 = 3/60 + 2/60 = 5/60 = 1/12 of the tank a minute, so it fills in 12 minutes.
A pipe can fill a tank in 6 hours. Because of a leak in the bottom, which on its own would empty the full tank in 12 hours, filling takes longer. How long does the pipe take to fill the tank with the leak?
Answer: C. 12 hours
The net rate is 1/6 − 1/12 = 1/12 of the tank an hour, so the tank fills in 12 hours.
A can do a job in 10 days and B in 15 days. They work together for 4 days, after which A leaves. In how many more days will B finish the remaining work?
Answer: D. 5 days
Together they do 1/10 + 1/15 = 1/6 of the job a day, so 4/6 = 2/3 in four days. One-third remains. B does 1/15 a day, so needs (1/3) ÷ (1/15) = 5 days.
A, B and C can finish a job alone in 10, 12 and 15 days respectively. In how many days will they finish it working together?
Answer: D. 4 days
1/10 + 1/12 + 1/15 = 6/60 + 5/60 + 4/60 = 15/60 = 1/4 of the job a day. Together they take 4 days.
A alone can do a job in 6 days and B alone in 12 days. They do the job together and are paid Rs 1,800 in all. What is A's share, if the money is divided according to the work done?
Answer: A. Rs 1,200
Their rates are 1/6 and 1/12, a ratio of 2 : 1. Working the same number of days, A does two-thirds of the job and receives two-thirds of Rs 1,800, which is Rs 1,200.
8 men working 5 hours a day can finish a job in 12 days. In how many days can 10 men working 6 hours a day finish it?
Answer: C. 8 days
The job is 8 × 5 × 12 = 480 man-hours. Ten men at 6 hours a day supply 60 man-hours a day, so the job takes 480 ÷ 60 = 8 days.

FAQ

What is the formula when two people work together?

If they take a and b days alone, together they take (a × b) ÷ (a + b) days. For 12 and 18 days this is 216 ÷ 30 = 7.2 days.

How are wages divided when people work together?

In proportion to the work each one did. If both work for the same number of days, that is the ratio of their daily rates, which is the inverse of the ratio of the times they would take alone.

How do pipes and cisterns differ from time and work?

They do not. A filling pipe has a positive rate, a leak or outlet has a negative rate, and the rates are added in the same way.

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