Question

Two pipes A and B can fill a tank in 12 minutes and 15 minutes respectively while a third pipe C can empty the full tank in 20 minutes. All the three pipes are opened in the beginning but pipe C is closed 6 minutes before the tank is filled. In what time will the tank is full?

• A. 15 minutes
• B. 10 minutes
• C. 7 minutes
• D. 17 minutes

Hint:

All three pipes fill \(\frac{1}{10}\) per minute. A and B alone fill \(\frac{3}{20}\) per minute for the last 6 minutes.

Answer 1

The Correct Option is C

Step 1: Pick a convenient capacity.
The times are 12, 15 and 20, so take the tank capacity as 60 units (the LCM).
Rate of A = 5 units per minute, rate of B = 4 units per minute, rate of C = -3 units per minute.

Step 2: Work on the last 6 minutes first.
In the last 6 minutes only A and B work. They fill $(5 + 4) \times 6 = 54$ units.

Step 3: Find what remains for the first part.
The tank holds 60 units, so the first part must fill $60 - 54 = 6$ units. In the first part all three pipes work, with net rate $5 + 4 - 3 = 6$ units per minute.
Time for the first part $= \frac{6}{6} = 1$ minute.

Step 4: Add the times.
Total time $= 1 + 6 = 7$ minutes.

Final Answer:
The tank is full in 7 minutes. \[ \boxed{7 \text{ minutes}} \]