Question

Two taps are running continuously to fill a tank. The 1st tap could have filled it in 5 hours by itself and the second one by itself could have filled it in 20 hours. But the operator failed to realise that there was a leak in the tank from the beginning which caused a delay of one hour in the filling of the tank. Find the time in which the leak would empty a filled tank.

Answer 1

It takes 20 hours to empty a filled tank due to leakage.

Given:

Time taken by 1st tap to fill the tank = 5 hours

Time taken by 2nd tap to fill the tank = 20 hours

To Find:

Time taken to empty a filled  tank due to leakage.

Solution:

Time taken per hour by both the taps without leakage is

$\frac{1}{5} +\frac{1}{20} \\\\\frac{4+1}{20} \\\\\frac{5}{20} \\\\\frac{1}{4}$

Therefore, It takes 4 hours to fill the tank by both the taps.

But, due to leakage there is a delay of one hour in filling the tank.

Hence , it takes 5 hours to fill the tank by both the taps due to leakage.

Now,the time taken per hour to empty a filled tank is

$\frac{1}{4} -\frac{1}{5} \\\\\frac{5-4}{20} \\\\\frac{1}{20}$

Therefore,it takes 20 hours to empty a filled tank due to leakage.

Answer 2

It takes 20 hours to empty a filled tank due to leakage.

Given,

Time taken by 1st tap to fill the tank = 5 hours

Time taken by 2nd tap to fill the tank = 20 hours

To Find,

Time taken to empty a filled tank due to leakage.

Solution,

Time taken per hour by both the taps without leakage is 1/5+1/20 = 1/4

Therefore, It takes 4 hours to fill the tank with both the taps.

But, due to leakage, there is a delay of one hour in filling the tank.

Hence, it takes 5 hours to fill the tank by both the taps due to leakage.

Now,

The time taken per hour to empty a filled tank is 1/4-1/5 = 1/20

Hence it takes 20 hours to empty a filled tank due to leakage.

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