Question

Three pipes $X,$ $Y$ and $Z$ can fill a tank from empty to full in $10$ minutes, $20$ minutes, and $40$ minutes respectively. When the tank is empty, all the three pipes are opened. $X,$ $Y$ and $Z$ discharge chemical solutions $P,$ $Q$ and $R$ respectively. What is the proportion of the solution $Q$ in the liquid in the tank after $5$ minutes?

• A. $\frac{7}{8}$
• B. $\frac{2}{7}$
• C. $\frac{5}{7}$
• D. $\frac{1}{4}$

Answer 1

The correct option is B $\frac{2}{7}$

Part filled by $(X+Y+Z)$ in $5$ minutes
$=5(\frac{1}{10}+\frac{1}{20}+\frac{1}{40})=\frac{7}{8}$
Part filled by $Y$ in $5$ minutes $=\frac{5}{20}=\frac{1}{4}$
$\therefore$ Required ratio $=\frac{1/4}{7/8}=\frac{2}{7}$