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

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, alternatively, with pipe A. In how much 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 tank be LCM (12, 15, 20) = 60 litres Now, Tank filled by A in 1 hour = 60/12 = 5 litres Tank filled by B in 1 hour = 60/15 = 4 litres Tank empty by C in 1 hour = 60/20 = 3 litres Now, According to the question, For first hour pipe A and B is opened = (5 + 4) litres = 9 litres For second hour pipe A and C is opened = (5 + 3) litres = 8 litres Hence, for every 2 hours, volume filled in the tank = (9 + 8) litres = 17 litres So, in (2 × 3) = 6 hours,volume of the tank filled = 3 × 17 = 51 litres The remaining volume to be filled = (60 – 51) = 9 litres Again in the 7^th hour, A and B are opened and fill the remaining tank in time = 9/9 = 1 hour Now, the time taken to fill the tank = 6 hour + 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, alternatively, with pipe A. In how much 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 tank be LCM (12, 15, 20) = 60 litres

Now,

Tank filled by A in 1 hour = 60/12 = 5 litres

Tank filled by B in 1 hour = 60/15 = 4 litres

Tank empty by C in 1 hour = 60/20 = 3 litres

Now,

According to the question,

For first hour pipe A and B is opened = (5 + 4) litres = 9 litres

For second hour pipe A and C is opened = (5 + 3) litres = 8 litres

Hence, for every 2 hours, volume filled in the tank = (9 + 8) litres = 17 litres

So, in (2 × 3) = 6 hours,volume of the tank filled = 3 × 17 = 51 litres

The remaining volume to be filled = (60 – 51) = 9 litres

Again in the 7^th hour, A and B are opened and fill the remaining tank in time = 9/9 = 1 hour