Mark againts the correct answer in the following: A pump can fill… - Vidyadip

MCQ

Mark againts the correct answer in the following: $A$ pump can fill a cistern in $2$ hours. Due to a leak in the tank it takes $2\frac{1}{3}$ hours to fill it. The leak can empty the full tank in:

A
$7$ hours.
✓
$14$ hours.
C
$8$ hours.
D
$3$ hours.

✓

Answer

Correct option: B.

$14$ hours.

$A$ pump fills a tank in $2$ hours.
Part of tank filled by the pump in one hour $=\frac{1}{2}$
Let $x$ hours be the time required for water to leak from the cistern.
Part of tank drained by the leak in one hour $=-\frac{1}{\text{x}}$
ime required to fill the leaking cistern $=2\frac{1}{3}=\frac{7}{3}$ hours.
Part of tank stored with water in one hour $=\frac{3}{7}$
$\Rightarrow\frac{3}{7}=\frac{1}{2}-\frac{1}{\text{x}}$
$\frac{1}{\text{x}}=\frac{1}{2}-\frac{3}{7}=\frac{7-6}{14}=\frac{1}{14}$
$\text{x}=14$ hours.

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