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 to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?

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

Answer 1

Answer: (D)

$30$ min

Part filled by $(A+B)$ in $1$ minute $=\left(\frac{1}{60}+\frac{1}{40}\right)=\frac{1}{24}$.
Suppose the tank is filled in x minutes.
Then, $\frac{x}{2}\left(\frac{1}{24}+\frac{1}{40}\right)=1$
$\Rightarrow \frac{x}{2}\times \frac{1}{15}=1$
$\Rightarrow x=30$ min.