Given:

Time taken by pipe A = 20 minutes

Time taken by pipe B = 30 minutes

Time taken by pipe C = 40 minutes

Calculation:

Let the total capacity of the tank be LCM (20, 30, 40) = 120 litres

Now,

Tank filled by A in 1 minute = 120/20

⇒ 6 litre/min

Tank filled by B in 1 minute = 120/30

⇒ 4 litre/min

Tank filled by C in 1 minute = 120/40

⇒ 3 litre/min

Tank filled by (A + B + C) in 1 minute = (6 + 4 + 3)

⇒ 13 litre/min

Now,

According to the question,

For first minute pipe, A is opened = 6 litre

For second-minute pipe, B is opened = 4 litre

For third-minute pipe, C is opened = 3 litre

For fourth minute pipe, A is opened = 6 litre

For fifth-minute pipe, B is opened = 4 litre

For sixth-minute pipe, C is opened = 3 litre

Similarly, So…. On

Now,

We conclude that –

3 minutes = 13 litre

× 9                × 9

27 min   =      117 litre

Now,

The remaining work = 120 – 117

⇒ 3 litre

Now,

Again 28th minute A will be opened and fill the remaining tank

⇒ 3/6

⇒ 1/2

Now,

The tank fills in = (27 minute + ½ minute)

⇒ 55/2 minutes

∴ The tank will be filled in 55/2 minutes.