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A tank fills completely in 2 hours if both the taps are open. If only one of the taps is open at the given time, the smaller tap takes 3 hours more than the larger one to fill the tank. How much time does each tap take to fill the tank completely?

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Let the larger tap take x hours to fill the tank completely.

∴ Part of tank filled by the larger tap in 1 hour = 1/x

Also, the smaller tap takes (x + 3) hours to fill the tank completely.

∴ Part of tank filled by the smaller tap in 1 hour = 1/(x + 3)

∴Part of tank filled by both the taps in 1 hour

\(=(\frac{1}{x} + \frac{1}{x + 3})\)

But, the tank gets filled in 2 hours by both the taps.

∴ Part of tank filled by both the taps in 1 hour = 1/2

According to the given condition,

By using the property, if the product of two numbers is zero, then at least one of them is zero, we get

∴ x – 3 = 0 or x + 2 = 0 

∴ x = 3 or x = -2

But, time cannot be negative.

∴ x = 3 and x + 3 = 3 + 3 = 6

∴ The larger tap takes 3 hours and the smaller tap takes 6 hours to fill the tank completely.

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