Question

. A pipe can fill a cistern in 9 hours. Due to a leak in its bottom, the cistern fills up in
10 hours. If the cistern is full, in how much time will it be emptied by the leak?
please solve it and follow mm e​

Answer 1

Solution :

A pipe can fill a cistern in 9 hours.

Due to a leak in its bottom, the cistern fills up in 10 hours.

Let us assume that the leak drains the water at a certain rate such that the tank will be emptied in x hours .

Work done in 1 hour :

( a ) By Pipe : ⅑

( b ) By Leak : - 1/x

Total time to fill the tank - 10 hrs [ In 1 hour therefore ⅒ th of the tank is filled ]

> ⅑ - 1/x = ⅒

> 1/x = ⅒ - ⅑

> 1/x = 1/90

> x = 90 .

Thus the leak drains the water from the tank in 90 hours.

This is the required answer.

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Answer 2

Answer:

Given :-

• A pipe can fill a cistern in 9 hours.
• Due to leak cistern fill in 10 hours

To Find :-

the cistern is full, in how much time will it be emptied by the leak?

Solution :-

Let's assume the time be x

Work done in 1 hour by pipe = ⅑

Work done by leak = 1/x

Now,

Total time = ⅒

$\sf \: \dfrac{1}{9} - \dfrac{1}{x} = \dfrac{1}{10}$

$\sf \dfrac{1}{x} = \dfrac{1}{10} - \dfrac{1}{9}$

$\sf \dfrac{1}{x} \: = \dfrac{1}{90}$

By reciprocal we get

$\sf \: x \: = 90 \: Hours$

Hence :-

Time taken is 90 hours