Question

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?

Answer 1

If a tank takes 16 hrs to fill and due to leak it takes 4 mores hrs to fill then a full tank can be emptied by the leak in 80 hrs.

Step-by-step explanation:

It is given that,  

A tank takes normally 16 hrs to fill

So, in 1 hour, the tank will fill = $\frac{1}{16}$th part

Also, due to a leak at the bottom of the tank, it takes 4 more hours, i.e., 4+16 = 20 hrs to fill, so,  

Along with the leakage, in 1 hr, the tank will manage to fill = $\frac{1}{20}$th part

Let the time taken by the leakage to empty the tank when it is full be “x” hrs.

According to the question we can write,

$\frac{1}{16}$ – $\frac{1}{x}$ = $\frac{1}{20}$

⇒ $\frac{1}{x}$ = [$\frac{1}{16}$ – $\frac{1}{20}$]

⇒ $\frac{1}{x}$ = [$\frac{1}{16}$ – $\frac{1}{20}$]

⇒ $\frac{1}{x}$ = $\frac{5-4}{80}$

⇒ $\frac{1}{x}$ = $\frac{1}{80}$

Thus, the leak takes 80 hrs to empty the tank when it is full.

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