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. $\frac{xyz}{2(xz+xy-yz)}$
• B. $\frac{2xyz}{xy+yz-xy}$
• C. $\frac{2xyz}{xz+xy-yz}$
• D. $\frac{xyz}{xy+yz-xy}$

Answer 1

Answer: (C)

$\text{ Let capacity of tank }=V{m}^3$
$\text{ and }\text{ A delivers }@Q_1{m}^3/min.$
$B\text{ delivers }@Q_2{m}^3/min$
$\text{ C delivers }@Q_3{m}^3/min.$
$\text{ Now, }A+B\text{ together }\to z\text{ minutes }$
$A+C\text{ together }\to y\text{ minutes }$
$B+C\text{ together }\to x\text{ minutes }$


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)
$(4)+(5)-(6)$
$2Q_1=\frac{V}{z}+\frac{V}{y}-\frac{V}{x}$
$\frac{2Q_1}{V}=\frac{yx+zx-yz}{xyz}$
$\frac{V}{Q_1}=\frac{2xyz}{xy+xz-yz}$