Question

There are two pipes in a tank if pipe A is opened the tank will be filled in 10 minutes and if pipe B is opened it will be filled in 15 minutes. If both are open together in how many minutes will it be filled ?

• A. 12 minutes
• B. 6 minutes
• C. 8 minutes
• D. 7.5 minutes

Answer 1

Answer:

B. 6 minutes

Understanding Pipe Filling Problems

This is a classic 'Time and Work' problem, commonly found in competitive exams. The core concept is to determine the rate at which each pipe works and then combine their rates.

Pipe A's Rate

• Pipe A can fill the tank in 10 minutes.

• Therefore, in 1 minute, Pipe A fills 1/10th of the tank. This is its rate of work.

Pipe B's Rate

• Pipe B can fill the tank in 15 minutes.

• Therefore, in 1 minute, Pipe B fills 1/15th of the tank. This is its rate of work.

Combined Rate

• When both pipes are opened together, their rates of filling add up.

• Combined rate per minute = (Rate of Pipe A) + (Rate of Pipe B)

• Combined rate = 1/10 + 1/15

• To add these fractions, find a common denominator, which is 30.

• Combined rate = (3/30) + (2/30) = 5/30

• Simplifying this fraction gives 1/6.

• This means that together, both pipes fill 1/6th of the tank in 1 minute.

Time to Fill Together

• If 1/6th of the tank is filled in 1 minute, then the entire tank (which is 1 unit) will be filled in the reciprocal of this rate.

• Time = 1 / (Combined Rate)

• Time = 1 / (1/6) = 6 minutes.