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?

11 hour
22 hours
36 hours
48 hours

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let the cistern be filledby pipe A alone in x hours . \\ Then, pipe B will fill it in (x + 6) hours \\ ∴ \frac{1}{x} + \frac{1}{(x + 6)} = \frac{1}{4} \\ \Rightarrow \frac{x + 6 + x}{x (x + 6)} = \frac{1}{4} \\ \Rightarrow x^{2} - 2 x - 24 = 0 \\ \Rightarrow (x - 6) (x + 4) = 0 \\ \Rightarrow x = 6. [neglecting the negative value of x] \end{aligned}

$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{cistern}}\,{\text{be}}\,{\text{filledby}}\,{\text{pipe}}\,A\,{\text{alone}}\,{\text{in}}\,x\,{\text{hours}}. \cr & {\text{Then,}}\,{\text{pipe}}\,B\,{\text{will}}\,{\text{fill}}\,{\text{it}}\,{\text{in}}\,\left( {x + 6} \right)\,{\text{hours}} \cr & \therefore \frac{1}{x} + \frac{1}{{\left( {x + 6} \right)}} = \frac{1}{4} \cr & \Rightarrow \frac{{x + 6 + x}}{{x\left( {x + 6} \right)}} = \frac{1}{4} \cr & \Rightarrow {x^2} - 2x - 24 = 0 \cr & \Rightarrow \left( {x - 6} \right)\left( {x + 4} \right) = 0 \cr & \Rightarrow x = 6.\,\,\left[ {{\text{neglecting}}\,{\text{the}}\,{\text{negative}}\,{\text{value}}\,{\text{of}}\,x} \right] \cr}$