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?
1 hour
2 hours
6 hours
8 hours
Explanation:
Let the cistern be filled by pipe A alone in $ x $ hours.
Then, pipe B will fill it in $\left( x + 6\right)$ hours.
$\therefore \dfrac{1}{x} $+$ \dfrac{1}{(x + 6)} $=$ \dfrac{1}{4} $
$\Rightarrow \dfrac{x + 6 + x}{x(x + 6)} $=$ \dfrac{1}{4} $
$\Rightarrow x $2 - 2$ x $ - 24 = 0
$\Rightarrow$ $\left( x -6\right)$$\left( x + 4\right)$ = 0
$\Rightarrow x $ = 6. [neglecting the negative value of $ x $]