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 empty tanker if only $B$ is used in the first-half of the time and $A$ and $B$ are both used in the second-half of the time ?

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

Answer 1

The correct option is D $30$

Part of tanker fill by the pipe A in 1 minute $=\frac{1}{60}$

Part of tanker fill by the pipe B in 1 minute $=\frac{1}{40}$

Let the time taken to fill the tank is $2x$ minute.

$\therefore$ Part of tanker filled $=\frac{1}{40}\times x+(\frac{1}{40}+\frac{1}{60})x=1$

$\Rightarrow \frac{x}{40}+\frac{(2+3)}{120}x=1$

$\Rightarrow \frac{x}{40}+\frac{x}{24}=1$

$\Rightarrow \frac{3x+5x}{120}=1$

$\Rightarrow x=\frac{120}{8}=15$ min

$\therefore$ Time taken to fill the tank$=2x=2\times 15=30$ min