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 chemicals 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

Answer: (B)

$\frac{6}{11}$

If all three pipes are opened

$\therefore$ in $1$ min the tank fills

$(\frac{1}{30}+\frac{1}{20}+\frac{1}{10})=\frac{2+3+6}{60}=\frac{11}{60}$

$\frac{11}{60}$ part is filled in $1$ min

$\frac{11\times 3}{60}=\frac{11}{20}$ part is filled in $3$ min

$\frac{11}{20}$ park of tank is filled by $A$,$B$&$C$

C can fill $\frac{1}{10}$ part in $1$ min

C can fill $\frac{3}{10}$ part in $3$ min

C can filled $\frac{3}{10}\times \frac{20}{11}$ in 3 min

$=\frac{6}{11}$