Question

A tap can fill a tank in $6$ hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

• A. $3$ hrs $15$ min
• B. $3$hrs $45$min
• C. $4$hrs
• D. $4$hrs $15$min

Answer 1

The correct option is B $3$hrs $45$min

Time taken by one tap to fill half of the tank$=3$ hrs.
Part time by the four taps in $1$ hour$=(4\times \frac{1}{6})=\frac{2}{3}$.
Remaining part$=\left(1-\frac{1}{2}\right)=\frac{1}{2}$.
$\therefore \frac{2}{3}:\frac{1}{2}::1:x$
$\Rightarrow x=\left(\frac{1}{2}\times 1\times \frac{3}{2}\right)=\frac{3}{4}$ hours i.e., $45$ mins.
So, total time taken $=3$hrs. $45$ mins.