GATE CH 2022 | GA Question: 3

Question

Pipes $\text{P}$ and $\text{Q}$ can fill a storage tank in full with water in $10$ and $6$ minutes, respectively. Pipe $\text{R}$ 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)?

• A. $26.8$
• B. $60.0$
• C. $120.0$
• D. $127.5$

Answer 1

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

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

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

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

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

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

$\Rightarrow 17x = 34 \times 60$

$\Rightarrow {\color{Blue}{\boxed{x = 120\;\text{litres}}}}$

$\therefore$ The capacity of the storage tank (in litres) is $120.$

Correct Answer $:\text{C}$

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

Answer 2

Let tank storage M litres .

P can add water to the tank = M/10 litres per min,

So in 60 min P can add water to the tank = 60*M/10 =6M litres.

Similarly Q can add water to the tank in 60 min = 60*M/6 = 10M litres .

Now tank was already full .

So, M+(6M+10M) = 34*60

> 17M = 2040

> M = 120

i.e: Tank storage was 120 Litres.