Question

One tank can be filled up by two taps in $6$ hours. The smaller tap alone takes $5$ hours more than the bigger tap alone. Find the time required by each tap to fill the tank separately.

• A. $15$ hrs and $10$ hrs
• B. $12$ hrs and $13$ hrs
• C. $21$ hrs and $4$ hrs
• D. $11$ hrs and $14$ hrs

Answer 1

The correct option is A $15$ hrs and $10$ hrs

Let the tap to fill the tank be $x$.
Smaller tap alone takes $5$ hours more than the bigger tap alone = $\frac{1}{x+5}$
Bigger tap can fill the tank = $\frac{1}{x}$
One tank can be filled up by two taps = $\frac{1}{x}+\frac{1}{x+5}=\frac{1}{6}$
$\Rightarrow \frac{2x+5}{x^2+5x}=\frac{1}{6}$
$\Rightarrow 12x+30=x^2+5x$
$x^2-7x-30=0$
Using $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ to get the value for $x$
$\Rightarrow \frac{7\pm \sqrt{(-7{)}^2-4\times 1\times (-30)}}{2\times 1}$
$\Rightarrow \frac{7\pm \sqrt{169}}{2}$
$\Rightarrow \frac{7\pm 13}{2}$
$x=10$, $x=-3$
$x$ cannot be negative.
The time required by each tap to fill the tank separately = 15 hours and 10 hours.