Question
During rainy season, huge inflow of water takes place
into a reservoir. Measures are taken to clear the reservoir while water keeps flowing into it at a constant rate. It has been observed that seven and five men can clear the reservoir in 20 and 50 days, respectively, with the initial quantity of water in the reservoir being 24 and 36 kilolitres, respectively. What is the rate of inflow of water into the reservoir in litres per day?Solution
Let each day x kiloliters of water flows into the reservoir. In 20 days 7 men clear 24 kl + 20x kl In 1 day 1 man clear (24 kl + 20x kl)/(7 × 20) Similarly, In 50 days 5 men clear 36 kl + 50x kl In 1 day 1 man clear (36 kl + 50x kl)/(5 × 50) According to the concept, (24 kl + 20x kl)/(7 × 20) = (36 kl + 50x kl)/(5 × 50) ⇒ (24 kl + 20x kl)/14 = (36 kl + 50x kl)/25 ⇒ 600 kl + 500x kl = 504 kl + 700x kl ⇒ 200x kl = 96 kl ⇒ x = 96/200 Rate of water inflow = 96/200 kiloliters or 96/200 × 1000 = 480 liters ∴ The rate of inflow of water into the reservoir in litres per day is 480 liters
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