Question

A tank has three independent inlet pipes, A, B and C. A and B together will fill the tank in z minutes, A and $C$ together will fill the tank in $y$ minutes and $B$ and $C$ together will fill the tank in $x$ minutes. The time taken by the inlet pipe A alone, to fill the tank will be

• A. $\frac{x y z}{2(x z+x y-y z)}$
• B. $\frac{2 x y z}{x y+y z-x y}$
• C. $\frac{2 x y z}{x z+x y-y z}$
• D. $\frac{x y z}{x y+y z-x y}$

Answer 1

Answer: (C)

$\text { Let capacity of tank }= V m ^3$
$\text { and } \text { A delivers } @ Q _1 m ^3 / min .$
$ B \text { delivers } @ Q _2 m ^3 / min $
$ \text { C delivers } @ Q _3 m ^3 / min .$
$\text { Now, } A + B \text { together } \rightarrow z \text { minutes }$
$ A + C \text { together } \rightarrow y \text { minutes } $
$ B + C \text { together } \rightarrow x \text { minutes }$


Now,
$Q_1+Q_2=\frac{V}{z} $ ....(4)
$Q_1+Q_3=\frac{V}{y} $ ...(5)
$Q_2+Q_3=\frac{V}{x}$ ...(6)
$(4)+(5)-(6)$
$2 Q_1 =\frac{V}{z}+\frac{V}{y}-\frac{V}{x} $
$\frac{2 Q_1}{V} =\frac{y x+z x-y z}{x y z} $
$\frac{V}{Q_1} =\frac{2 x y z}{x y+x z-y z}$