Time taken by pipe B to fill the tank alone is $30 imes \frac{2}{3} = 20$ hours. Let the total capacity of the tank be 60 units. The efficiencies of pipes A, B, and C are 6, 3, and 2 units/hour respectively. Calculate the volume (approx.) of the initially empty tank P filled in 1 hour when all three pipes are opened simultaneously. (Time taken by pipe C is 30 hours.)

Question

Time taken by pipe B to fill the tank alone is $30 	imes \frac{2}{3} = 20$ hours. Let the total capacity of the tank be 60 units. The efficiencies of pipes A, B, and C are 6, 3, and 2 units/hour respectively. Calculate the volume (approx.) of the initially empty tank P filled in 1 hour when all three pipes are opened simultaneously. (Time taken by pipe C is 30 hours.)

Accepted Answer

**Solution:**

1. Given:
   - Time taken by pipe B to fill the tank alone = $30 	imes \frac{2}{3} = 20$ hours
   - Let total capacity of tank = 60 units

2. Efficiencies (units/hour):
   - Pipe A = 6 units/hour
   - Pipe B = 3 units/hour
   - Pipe C = 2 units/hour (since time taken by pipe C is 30 hours, efficiency = $\frac{60}{30} = 2$ units/hour)

3. When all three pipes are opened simultaneously, the net filling rate = (A + B - C) units/hour
   $$6 + 3 - 2 = 7 	ext{ units/hour}$$

4. Volume filled in 1 hour:
   $$\frac{7}{60} 	imes 38808 = 4527.6 \approx 4528 	ext{ m}^3$$

**Answer:** 4528 m³

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