Question

A large tanker can be filled by two pipes $A$ and $B$ in $60$ minutes and $40$ minutes respectively, How many minutes will it take o fill the tanker form empty state, if $B$ is used for half the time and $A$ and $B$ full it for the other half ?

• A. $15$ minutes
• B. $20$ minutes
• C. $27.5$ minutes
• D. $30$ minutes

Answer 1

The correct option is D $30$ minutes

Let the total time taken to fill the tank be $x$ minutes.

Then, work done by $B$ in half hour $+$ work done by $(A+B)$ in half hour $=1$.

$(\frac{1}{40}\times \frac{x}{2})+(\frac{1}{60}+\frac{1}{40})\times \frac{x}{2}=1$

$\Rightarrow \frac{x}{80}+\frac{x}{48}=1$

$\Rightarrow \frac{3x+5x}{240}=1$

$\Rightarrow 8x=240$

$\Rightarrow x=30$ min