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. $1$ hours
• B. $2$ hours
• C. $6$ hours
• D. $8$ hours

Answer 1

Answer: (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.

$\therefore \frac{1}{x}+\frac{1}{x+6}=\frac{1}{4}$

$\Rightarrow \frac{x+6+x}{x(x+6)}=\frac{1}{4}$

$\Rightarrow x^2-2x-24=0$

$\Rightarrow x^2-6x+4x-24=0$

$\Rightarrow x(x-6)+4(x-6)=0$

$\Rightarrow (x-6)(x+4)=0$

If we neglect the negative value then $x=6$

Hence the cistern be filled by pipe $A$ alone in $6$ hrs.