Discussion

Explanation:

Let the total capacity of tank = LCM(20, 30, 15) = 60 units

∴ Efficiency of pipe A = 60/20 = 3 units/minute
∴ Efficiency of pipe B = 60/30 = 2 units/minute
∴ Efficiency of pipe C = 60/15 = - 4 units/minute (-ve indicates that pipe C empties the tank)

Now work done in 1 cycle (i.e., 3 minutes) = 3 + 2 – 4 = 1 units

Now this becomes a little tricky situation because C is emptying a large amount of water which is filled by A and B.

⇒ Number of cycles required to complete the work = 60/1 = 60 cycles.

Since C is emptying the tank, let’s break the last few cycles.

Work done till 53 cycles (i.e., in 53 × 3 = 159 minutes) = 53 × 1 = 53 units.

In 54^th cycle,
In next 2 minutes A and B will fill 3 + 2 = 5 units. Hence, the total work done = 58 units till 161 minutes.
In next 1 minute C will empty 4 units. Hence, the total work done = 54 units till 162 minutes.

In 55^th cycle,
In next 2 minutes A and B will fill 3 + 2 = 5 units. Hence, the total work done = 59 units till 164 minutes.
In next 1 minute C will empty 4 units. Hence, the total work done = 55 units till 165 minutes.

In 56^th cycle,
In next 2 minutes A and B will fill 3 + 2 = 5 units. Hence, the total work done = 60 units till 167 minutes.
Now, since the work is completed, pipes will no longer be operated.

∴ It takes 167 minutes for the tank to be completely filled.

Hence, 167.

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