Question

Two taps can fill a tank in 20 minutes and 30 minutes respectively. There is an outlet tap at exactly half level of that rectangular tank which can pump out 50 litres of water per minute. If the outlet tap is open, then it takes 24 minutes to fill an empty tank. What is the volume of the tank?

• A. 1800 litres
• B. 1500 litres
• C. 1200 litres
• D. 1400 litres

Answer 1

The Correct Option is D

Two taps fill the tank at rates of \(\frac{V}{20}\) and \(\frac{V}{30}\) liters per minute, and an outlet removes 50 liters per minute when the tank is half full.

In the first 12 minutes, the taps fill half the tank:  
 \(\left( \frac{V}{12} \right) \times 12 = \frac{V}{2}\).
 
In the next 12 minutes (with the outlet open), the filling rate becomes \(\frac{V}{12} - 50\) liters per minute.  

Setting this equal to half the tank:

\(\Rightarrow\;\)\(\frac{V}{12} \times 12 - 600 = \frac{V}{2}\)

\(\Rightarrow\;\)\(V = 1440\) liters.

Thus, the tank's volume is 1440 liters.