Correct Answer - Option 4 : 55/2
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.