Three pipes A, B, and C can fill a tank in 12 hours, 15 hours, and 20

1.	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 hours2. 8 hours3. 6 hours4. 7 hours5. None of these
Answer» 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

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 hours2. 8 hours3. 6 hours4. 7 hours5. None of these

Answer» 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