Two pipes, A and B, can fill a tank in 10 minutes and 20 minutes, respectively. Pipe C can empty the tank in 30 minutes. All three pipes are opened together at the start, but pipe C is closed 2 minutes before the tank is filled. In what time will the tank be full (in minutes)?

Question

Accepted Answer

Let the total capacity of the tank be 60 units (LCM of 10, 20, 30).

Pipe A fills 60/10 = 6 units per minute.
Pipe B fills 60/20 = 3 units per minute.
Pipe C empties 60/30 = 2 units per minute.

When all three pipes are open, net fill per minute = 6 + 3 - 2 = 7 units per minute.

Let the total time taken to fill the tank be T minutes.
For the last 2 minutes, only A and B are open (C is closed), so fill rate = 6 + 3 = 9 units per minute.

So, for (T - 2) minutes, all three pipes are open (net 7 units/min), and for last 2 minutes, only A and B are open (9 units/min).

Total work done = 60 units:
7 × (T - 2) + 9 × 2 = 60
7T - 14 + 18 = 60
7T + 4 = 60
7T = 56
T = 8

But let's check this carefully:
If T = 8 minutes, then for 6 minutes all three are open, for last 2 minutes only A and B.
Work done in 6 minutes: 7 × 6 = 42 units
Work done in last 2 minutes: 9 × 2 = 18 units
Total = 42 + 18 = 60 units
So, T = 8 minutes.

But the options do not match this calculation. Let's check the step-by-step again:
Let T = total time to fill the tank.
For (T - 2) minutes, all three pipes are open: 7 × (T - 2)
For last 2 minutes, only A and B: 9 × 2 = 18
So,
7(T - 2) + 18 = 60
7T - 14 + 18 = 60
7T + 4 = 60
7T = 56
T = 8

So, the correct answer is 8 minutes, but the answer key says 10. Let's check the calculation with a different approach:
Suppose the tank is filled in T minutes.
For (T - 2) minutes, all three pipes are open.
For last 2 minutes, only A and B.

Let x = time for which all three are open = T - 2
Work done in x minutes = 7x
Work done in last 2 minutes = 9 × 2 = 18
Total work = 7x + 18 = 60
7x = 42
x = 6
So, T = x + 2 = 8 minutes.

So, the correct answer is 8 minutes.

Therefore, the correct answer is option 3: 8.

Answer

Answer

Answer