Question

Two pipes $A$ and $B$ together can fill a cistern in $4$ hours. Had they been opened separately, then $B$ would have taken $6$ hours more than $A$ to fill the cistern. How much time will be taken by $A$ to fill the cistern separately?

• A. $1$ hour
• B. $4$ hours
• C. $6$ hours
• D. $8$ hours

Answer 1

The correct option is C $6$ hours

Let the cistern be filled by pipe $A$ alone in $x$ hours.
Then, pipe $B$ will fill it in $(x+6)$ hours.
$\therefore \frac{1}{x}+\frac{1}{x+6}=\frac{1}{4}$
$\Rightarrow \frac{x+6+x}{x(x+6)}=\frac{1}{4}$
$\Rightarrow 8x+24=x^2+6x$
$\Rightarrow x^2-2x-24=0$
$\Rightarrow (x-6)(x+4)=0$
$\Rightarrow x=6$ [Neglecting the negative value]
So, pipe $A$ alone will fill the cistern in $6$ hours while pipe $B$ alone will fill the cistern in $12$ hours.