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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?

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? Correct Answer 480

Given:

The initial quantity of water in the reservoir is 24 and 36 kilolitres

Concept used:

Efficiency = Total work/(M × T)

Calculation: 

Let each day x kiloliters water flows into the reservoir.

In 20 days 7 men fill 24 kl + 20x kl

In 1 day 1 man fills (24 kl + 20x kl)/(7 × 20)

Similarly,

In 50 days 5 men fill 36 kl + 50x kl

In 1 day 1 man fills (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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