Question

Three pipes $A,B$ and $C$ can fill a tank from empty to full in $30$ minutes, $20$ minutes, and $10$ minutes respectively. When the tank is empty, all the three pipes are opened. $A,B$ and $C$ discharge chemical solutions $P,Q$ and $R$ respectively. What is the proportion of the solution $R$ in the liquid in the tank after $3$ minutes?

• A. $\frac{5}{11}$
• B. $\frac{6}{11}$
• C. $\frac{7}{11}$
• D. $\frac{8}{11}$

Answer 1

The correct option is B $\frac{6}{11}$

Rate of filling the tank for A: $\frac{1}{30}$

Rate of filling the tank for B: $\frac{1}{20}$

Rate of filling the tank for C: $\frac{1}{10}$

Part filled by $(A+B+C)$ in $3$ minutes $3\left(\frac{1}{30}+\frac{1}{20}+\frac{1}{10}\right)$ $=(3\times \frac{11}{60})=\frac{11}{20}$.

Part filled by C in $3$ minutes $=\frac{3}{10}$.

$\therefore$ Required ratio$=\left(\frac{3}{10}\times \frac{20}{11}\right)=\frac{6}{11}$.