Question

A tank can be filled by pipe A in 2 hours and Pipe B in 6 hours. At 10 am, pipe A was opened. At what time will the tank be filled if pipe B is opened at 11 am?

• A. 12.45 AM
• B. 5 PM
• C. 11.45 AM
• D. 12 PM

Answer 1

Answer:

C. 11.45 AM

1. Determine individual filling rates:

   • Pipe A's rate = 1/2 tank per hour.

   • Pipe B's rate = 1/6 tank per hour.

2. Calculate work done by Pipe A alone:

   • Pipe A was opened at 10 am.

   • By 11 am (when Pipe B is opened), Pipe A has been working for 1 hour.

   • Work done by Pipe A in 1 hour = 1 * (1/2) = 1/2 of the tank.

3. Calculate the remaining work:

   • Total tank capacity = 1 (representing the whole tank).

   • Remaining work to be filled = Total capacity - Work done by A = 1 - 1/2 = 1/2 of the tank.

4. Calculate the combined filling rate of Pipe A and Pipe B:

   • From 11 am onwards, both pipes work together.

   • Combined rate = Rate of A + Rate of B = (1/2) + (1/6) tank per hour.

   • To add these fractions, find a common denominator (which is 6): (3/6) + (1/6) = 4/6 tank per hour.

   • Simplify the combined rate: 2/3 tank per hour.

5. Calculate the time taken to fill the remaining work:

   • Time = Remaining Work / Combined Rate

   • Time = (1/2) / (2/3) hours

   • Time = (1/2) * (3/2) = 3/4 hours.

6. Convert the time into minutes:

   • 3/4 hours = (3/4) * 60 minutes = 45 minutes.

7. Determine the final filling time:

   • The remaining 1/2 tank was filled starting from 11 am.

   • It took 45 minutes to fill the rest.

   • Therefore, the tank will be completely filled at 11 am + 45 minutes = 11:45 AM.