Question

Three pipes A, B and C can fill a tank in 12 hours. All the pipes started working together and after 3 hours, C is closed. If A and B can fill the remaining part in 10 hours, then the number of hours taken by C alone to fill the tank is.

• A. 100 hours
• B. 110 hours
• C. 120 hours
• D. 130 hours

Answer 1

The Correct Option is C

Let's determine how long pipe C alone would take to fill the tank by following these logical steps:

First, note that all pipes A, B, and C working together can fill the tank in 12 hours. Therefore, their combined rate of work is:

1/12 of the tank per hour.

The combined work done by A, B, and C in the first 3 hours is:

3 × 1/12 = 1/4 of the tank.

This means that 1/4 of the tank is filled by A, B, and C together in 3 hours, leaving 3/4 of the tank still to be filled.

Next, when pipe C is closed after 3 hours, pipes A and B finish the remaining 3/4 of the tank in 10 hours. Therefore, the combined rate of work of pipes A and B is:

(3/4) / 10 = 3/40 of the tank per hour.

This means A and B together can fill 3/40 of the tank per hour.

We know the combined rate of A, B, and C is 1/12 from earlier:

1/12 of the tank per hour.

Thus, the rate at which pipe C works is the difference between the combined rate of all three pipes and the rate of pipes A and B:

1/12 - 3/40.

Now, let's compute this difference by finding a common denominator:

1/12 = 10/120 and 3/40 = 9/120.

Therefore, the rate at which pipe C alone works is:

10/120 - 9/120 = 1/120 of the tank per hour.

Thus, pipe C alone can fill the entire tank in:

120 hours.