# 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,

+1 vote
32 views

closed

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?

by (35.1k points)
selected

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.