Question

A cistern can be filled by two pipes in 30 and 40 min respectively. Both the pipes are opened at once, when the first pipe must be turned off so that the tank may be just filled in 18 min ?

• A. 12.5 min
• B. 13.5 min
• C. 14.5 min
• D. 16.5 min

Answer 1

The correct option is D 16.5 min

Let the first pipe be turned off after x minutes, then work done by (First pipe in x min. + Second pipe in 18 min.) = 1
$\Rightarrow \frac{x}{30}+\frac{18}{40}=1$

$\Rightarrow \frac{4x+54}{120}=1$

$\Rightarrow 4x+54=120$

$\Rightarrow 4x=66$

$\Rightarrow x=\frac{66}{4}=16.5$ min.