Question

There are two pipes leading to a tank. If pipe A alone is opened, the tank will be filled in 15 minutes. If pipe B alone is opened, the tank will be filled in 10 minutes. Both pipes were opened together. After 2 minutes, pipe B was closed. How long should pipe A be left open to fill the rest of the tank?

• A. 10 minutes
• B. 7.5 minutes
• C. 5 minutes
• D. 12 minutes

Answer 1

Answer:

A. 10 minutes

Time and Work Problems - Pipe and Cisterns

Understanding the Concepts

• This problem falls under the Time and Work section, specifically dealing with pipes and cisterns.

• The core principle is to determine the rate at which each pipe fills the tank and then calculate the combined rate.

• Rate of work is often expressed as the fraction of the work done per unit of time.

Problem Breakdown and Solution

• Pipe A's Rate: If Pipe A fills the tank in 15 minutes, its rate is 1/15 of the tank per minute.

• Pipe B's Rate: If Pipe B fills the tank in 10 minutes, its rate is 1/10 of the tank per minute.

• Combined Rate (Initially): When both pipes are open, their combined rate is the sum of their individual rates: (1/15) + (1/10).

• To add these fractions, find a common denominator, which is 30: (2/30) + (3/30) = 5/30 or 1/6 of the tank per minute.

• Work Done in First 2 Minutes: Both pipes were open for 2 minutes. The amount of the tank filled in these 2 minutes is (Combined Rate) × (Time) = (1/6) × 2 = 2/6 or 1/3 of the tank.

• Remaining Work: The total capacity of the tank is considered 1 unit. After 2 minutes, the remaining portion to be filled is 1 - (1/3) = 2/3 of the tank.

• Pipe B is Closed: After 2 minutes, Pipe B is closed. Only Pipe A continues to fill the remaining part.

• Time for Pipe A to Fill Remaining: Pipe A's rate is 1/15 of the tank per minute. To fill the remaining 2/3 of the tank, the time required is (Remaining Work) / (Pipe A's Rate) = (2/3) / (1/15).

• Calculating this: (2/3) × (15/1) = 30/3 = 10 minutes.