Question

Three pipes A, B, and C can fill a tank in 12 hours, 15 hours, and 20 hours respectively. If pipe A is opened all the time and pipe B and C are open for one hour each alternately. Pipe B opened first then pipe C opened alternatively. At what time the tank will be full?

1. 9 hours
2. 8 hours
3. 6 hours
4. 7 hours
5. None of these

Answer 1

Correct Answer - Option 4 : 7 hours

Given:

Pipe A can fill a tank in = 12 hours

Pipe B can fill a tank in = 15 hours

Pipe C can fill a tank in = 20 hours

Calculation:

Let the total capacity of the tank be LCM (12, 15, 20) = 60 litres

Now,

Tank filled by A in 1 hour = 60/12

⇒ 5 litre/hour

Tank filled by B in 1 hour = 60/15

⇒ 4 litre/hour

Tank filled by C in 1 hour = 60/20

⇒ 3 litre/hour

Now,

According to the question,

For first-hour pipe A and B is opened = (5 + 4) litre

⇒ 9 litre

For second-hour pipe A and C is opened = (5 + 3) litre

⇒ 8

For third-hour pipe A and B is opened = (5 + 4) litre

⇒ 9 litre

For fourth-hour pipe A and C is opened = (5 + 3) litre

⇒ 8

Similarly, So…. On

Now,

We conclude that –

2 hours  =   17 litre

× 3               × 3

6 hours   =    51 litre

Now,

The remaining work = (60 – 51)

⇒ 9 litre

Again 7^th hour A and B are opened and fill the remaining tank

⇒ 9/9

⇒ 1 hour

Now,

The tank fills in = (6hour + 1 hour)

⇒ 7 hours

∴ The tank will be fill in 7 hours