Question

Two water taps together can fill a tank in $3\frac{1}{13}$ hours. The tap of longer diameter takes $3$ hours less then smaller one to fill the bank separately. Find the time(hrs) in which tap of smaller diameter can separately fill the tank.

• A. $5$
• B. $3$
• C. $8$
• D. None of these

Answer 1

The correct option is C $8$

Let time taken by tap of longer diameter be $x$ hours

Then time taken by tap of smaller diameter will be $x+3$ hours

Now, According to question

$\frac{1}{x}+\frac{1}{x+3}=\frac{13}{40}$

$\Rightarrow \frac{2x+3}{x\left(x+3\right)}=\frac{13}{40}$

$\Rightarrow 80x+120=13x^2+39x$

$\Rightarrow 13x^2-41x-120=0$

$\Rightarrow 13x^2+24x-65x-120=0$

$\Rightarrow x\left(13x+24\right)-5\left(13x+24\right)=0$

$\Rightarrow \left(13x+24\right)\left(x-5\right)=0$

$\Rightarrow x=\frac{-24}{13}$ or $x=5$

Since time cannot be negative

Therefore $x=5$

Hence, Time taken by tap of larger diameter is$5$ hours and time taken by tap of smaller diameter is $8$ hours