1 vote

Pipes $P$ and $Q$ can fill a storage tank in full with water in $10$ and $6$ minutes, respectively. Pipe $R$ draws the water out from the storage tank at a rate of $34$ litres per minute. $\text{P, Q and R}$ operate at a constant rate.

If it takes one hour to completely empty a full storage tank with all the pipes operating simultaneously, what is the capacity of the storage tank (in litres)?

- $26.8$
- $60.0$
- $120.0$
- $127.5$

0 votes

Let the capacity of the storage tank be $x \;\text{litres}.$

$\begin{array}{lccc} & \textbf{P} & \textbf{Q} & \textbf{R} \\ \text{Time:} & 10\;\text{minutes} & 6\;\text{minutes} & \\ \text{Capacity of tank:} & x \;\text{litres} & & \\ \text{Efficiency:} & \frac{x}{10} \;\text{litres/minute} & \frac{x}{6} \;\text{litres/minute} & 34 \;\text{litres/minute} \end{array}$

If it takes one hour to completely empty a full storage tank with all the pipes operating simultaneously.

Now, $\frac{x}{10} \times 60 + \frac{x}{6} \times 60 = 34 \times 60$

$\Rightarrow \frac{x}{10} + \frac{x}{6} = 34$

$\Rightarrow \frac{6x + 10x}{60} = 34$

$\Rightarrow 16x = 34 \times 60$

$\Rightarrow {\color{Blue}{\boxed{x = 127.5\;\text{litres}}}}$

$\therefore$ The capacity of the storage tank (in litres) is $127.5.$

Correct Answer $:\text{D}$

${\color{Magenta}{\textbf{PS:}}}\;{\color{Green}{\boxed{\text{Total work = Time} \; \times\; \text{Efficiency}}}}$

$\begin{array}{lccc} & \textbf{P} & \textbf{Q} & \textbf{R} \\ \text{Time:} & 10\;\text{minutes} & 6\;\text{minutes} & \\ \text{Capacity of tank:} & x \;\text{litres} & & \\ \text{Efficiency:} & \frac{x}{10} \;\text{litres/minute} & \frac{x}{6} \;\text{litres/minute} & 34 \;\text{litres/minute} \end{array}$

If it takes one hour to completely empty a full storage tank with all the pipes operating simultaneously.

Now, $\frac{x}{10} \times 60 + \frac{x}{6} \times 60 = 34 \times 60$

$\Rightarrow \frac{x}{10} + \frac{x}{6} = 34$

$\Rightarrow \frac{6x + 10x}{60} = 34$

$\Rightarrow 16x = 34 \times 60$

$\Rightarrow {\color{Blue}{\boxed{x = 127.5\;\text{litres}}}}$

$\therefore$ The capacity of the storage tank (in litres) is $127.5.$

Correct Answer $:\text{D}$

${\color{Magenta}{\textbf{PS:}}}\;{\color{Green}{\boxed{\text{Total work = Time} \; \times\; \text{Efficiency}}}}$