Question

Two Pipes can separately fill a tank in 12 minutes and 24 minutes respectively. A waste pipe empties the tank at the rate of 20 liters per minute. If all of them are opened at a time the tank is filled in 24 minutes. Then the capacity of that tank in liters is

• A. \(480\)
• B. \(420\)
• C. \(380\)
• D. \(240\)

Hint:

In pipe problems, convert everything into rate (work per minute) first before forming the equation.

Answer 1

The Correct Option is D

Concept: Net filling rate = Sum of filling rates – Waste pipe rate. Let tank capacity be: \[ x \text{ liters} \]

Step 1: Find filling rates.
First pipe: \[ \frac{x}{12}\text{ liters/min} \] Second pipe: \[ \frac{x}{24}\text{ liters/min} \] Waste pipe: \[ 20\text{ liters/min} \]

Step 2: Form net rate equation.
Tank fills in 24 minutes, so: \[ \text{Net rate}=\frac{x}{24} \] Thus: \[ \frac{x}{12}+\frac{x}{24}-20=\frac{x}{24} \]

Step 3: Simplify.
Take LCM \(24\): \[ \frac{2x+x}{24}-20=\frac{x}{24} \] \[ \frac{3x}{24}-20=\frac{x}{24} \] Multiply by 24: \[ 3x-480=x \] \[ 2x=480 \] \[ x=240 \] Thus, the capacity of the tank is: \[ \boxed{240 \text{ liters}} \]