Question

Taps $A$ and $B$ can fill in a tank in $12$ and $15$ min respectively. If both are opened and $A$ is closed after $3$ min how long will it take for $B$ to fill in the tank ?

• A. $8$ min $15$ s
• B. $8$ min $5$ s
• C. $7$ min $45$ s
• D. $8$ min $45$ s

Answer 1

The correct option is A $8$ min $15$ s

Tank filled by tab A in 1 minute$=\frac{1}{12}$

Tank filled by tab B in 1 minute$=\frac{1}{15}$

Tank filled by tab A and B ib 1 minute$=\frac{1}{12}+\frac{1}{15}=\frac{9}{60}$

Pipe A and B is opened for 3 minute

Then part filled by A and B in 3 minute$=\frac{9}{50}\times 3=\frac{9}{20}$

Remaining part$=1-\frac{9}{20}=\frac{11}{20}$

Time taken by B to fill this remaining part$=\frac{\frac{11}{20}}{\frac{1}{15}}$

$=\frac{11\times 15}{20}=\frac{33}{4}=8\frac{1}{4}$

$=8min15s$