Question

A tap can fill a tank in $15$ minutes Another tap can empty it in $20$ minutes. Initially the tank is empty. If both the taps start functioning then the time taken to fill the tank is

• A. $1$ hour
• B. $1$ hour $40$ min
• C. $90$ minutes
• D. $2$ hours

Answer 1

The correct option is A $1$ hour

Tap $A$ can fill the tank in $15$ minutes.

Then part of tank filled by Tap $A$ in $1$ minute $=\frac{1}{15}$

Tap $B$ can empty the tank in $20$ minutes.

Then part of tank empty by Tap $B$ in $1$ minute $=\frac{1}{20}$

If both the taps start functioning then part of the tank filled in $1$ minute=

$\frac{1}{15}-\frac{1}{20}=\frac{1}{60}$

Now,

$\frac{1}{60}$ part of the tank is filled in $1$ minute.

So, time taken to fill the whole tank = $1\times \frac{60}{1}=60$ minutes