CBSE Class 10 Mathematics Time and Work Notes Set 19

Time and Work

If a worker completes a job in n days, his one-day work is 1/n. If A and B take a and b days alone, together they take ab/(a + b) days, because their combined one-day work is 1/a + 1/b.
If the work is shared among workers of different efficiency, the wages are divided in the ratio of the work done. If A is k times as efficient as B, A takes 1/k of B's time.

Men, Days and Hours

Total work = men × days × hours per day (when all work at the same rate). So M1 D1 H1 = M2 D2 H2 for the same job. If workers are of different types (men, women, children), first convert the work to one type, for example 1 man = 4/3 women.
When some workers join or leave part-way, count the work in two stages and add; the work done in each stage is (number of workers × days × one-person rate).

Pipes and Cisterns

An inlet pipe fills a tank in x hours means it fills 1/x of the tank per hour; an outlet pipe empties 1/y per hour. With both open, the net rate is 1/x − 1/y.
If a leak makes the filling time longer, the leak empties the tank at the difference of the two rates. When pipes are opened alternately, work out one full cycle first and then deal with the last part separately.

Worked Examples

Illustration 1. A can finish a work in 12 days and B in 15 days. How long will they take together?
Answer:
Together: 1/12 + 1/15 = 9/60 = 3/20 per day.
They take 20/3 = 6 2/3 days.

Illustration 2. A pipe fills a tank in 6 hours and a leak empties it in 8 hours. How long to fill the tank with both working?
Answer:
Net rate = 1/6 − 1/8 = 1/24, so it takes 24 hours.

Illustration 3. 12 men can complete a work in 20 days working 8 hours a day. How many days will 16 men working 6 hours a day take?
Answer:
12 × 20 × 8 = 16 × D × 6, so D = 20 days.