Question

A pipe can fill an empty tank in 84 minutes. Due to leak at the bottom, it takes 2 hours to fill the tank. In what time will the leak alone empty the full tank? (a) 280 minutes (b) 200 minutes (C) 180 minutes (d) None of these ​

Answer 1

Given:

A pipe can fill an empty tank in 84 minutes. Due to a leak at the bottom, it takes 2 hours to fill the tank. At what time will the leak alone empty the full tank? (a) 280 minutes (b) 200 minutes (C) 180 minutes (d) None of these ​

To find:

At what time will the leak alone empty the full tank?

Solution:

A pipe can fill an empty tank in 84 minutes.

So, the part of the tank filled by the pipe in 1 min = $\frac{1}{84}$

Let's say the leak alone takes "x" minutes to empty the full tank.

So, the part of the tank emptied by the leak in 1 min = $\frac{1}{x}$

Due to a leak at the bottom, it takes 2 hours i.e., 120 minutes (∵ 1 hour = 60 minutes) to fill the tank. So, we can form the equation as,

[Part of the tank filled in 1 min] - [Part of the tank emptied in 1 min] = [Part of the tank filled due to the leak at the bottom]

$\bold{\frac{1}{84} - \frac{1}{x} = \frac{1}{120}}$

$\implies \frac{x \:-\: 84}{84x} = \frac{1}{120}$

$\implies 120(x \:-\: 84) = 84x$

$\implies 120x \:-\: 10080 = 84x$

$\implies 120x \:-\: 84x = 10080$

$\implies 36x = 10080$

$\implies \bold{x = 280\:minutes}$ ← option (a)

Thus, the leak alone will empty the full tank in → 280 minutes.

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Also View:

A tank is normally filled in 16 hours. Because of a leak at it's bottom, it takes 4 hours more to fill. How much time (in hours) will the leak take to empty the tank when it is full?

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Two pipes P and Q can fill a tank in 8 hours and 24 hours respectively. There is a leak that can empty the full tank in 12 hours. If the leak is actually at 2/3 of the height from the base, then how many hours will the empty tank will be filled if all pipes are opened simultaneously?​

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