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A pond is fitted with two pipes. The first pipe can fill the pond completely in 45 minutes and the second pipe can empty the full pond in one hour. If both the pipes are opened alternatively for one minute, then in how many hours the empty pond will be filled completely?

A pond is fitted with two pipes. The first pipe can fill the pond completely in 45 minutes and the second pipe can empty the full pond in one hour. If both the pipes are opened alternatively for one minute, then in how many hours the empty pond will be filled completely? Correct Answer 5 hours 53 minutes

Given:

The first pipe can fill the pond in 45 minutes,

The second pipe can empty the pond in 1 hour

Concept:

If a tap can fill a tank in x hours, then the tank filled by the tap in 1 hour = 1/x of the total tank.

Calculation:

Part of the pond filled in one minute

⇒ (1/45) – (1/60)

⇒ (4 – 3)/180

⇒ 1/180

(1/180) parts is filled in 1 minute

⇒ 1 – (1/45) = 44/45 parts is filled in (2 × 180 × 44)/45

⇒ 352 minutes

⇒ 5 hours 52 minutes

Remaining 1/45 parts will be filled in 1 minute

Total time taken = 5 hours 53 minutes

∴ The required time is 5 hours 53 minutes.

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