Question

There are two pipes leading to a tank. If pipe A alone is opened, the tank will be filled in 1 hour. If pipe B alone is opened, the tank will be filled in 1 hour 30 minute Both pipes were opened together. After 27 minute pipe B was closed. How long could pipe A left open to fill the rest of the tank?

• A. 20 minute
• B. 25 minute
• C. 15 minute
• D. 10 minute

Answer 1

Answer:

C. 15 minute

Time and Work Concepts for Competitive Exams

Understanding Rates of Work

• When a pipe can fill a tank in 'x' hours, its rate of filling is 1/x of the tank per hour.

• Conversely, if the rate is R per hour, the time taken to fill the tank is 1/R hours.

Problem Breakdown

• Pipe A fills the tank in 1 hour. Rate of Pipe A = 1/1 tank/hour.

• Pipe B fills the tank in 1 hour 30 minutes, which is equal to 1.5 hours or 3/2 hours. Rate of Pipe B = 1 / (3/2) = 2/3 tank/hour.

• When both pipes are open, their combined rate is the sum of their individual rates: Rate (A+B) = Rate(A) + Rate(B) = 1 + 2/3 = 5/3 tank/hour.

Calculating Work Done Together

• Both pipes are opened together for 27 minutes. Convert minutes to hours: 27 minutes = 27/60 hours = 9/20 hours.

• Work done by both pipes in 27 minutes = Combined Rate × Time = (5/3) × (9/20) = 45/60 = 3/4 of the tank.

Calculating Remaining Work

• The fraction of the tank filled is 3/4.

• The remaining fraction of the tank to be filled is 1 (whole tank) - 3/4 = 1/4 of the tank.

Time Taken by Pipe A to Fill Remaining Work

• After 27 minutes, Pipe B is closed. Only Pipe A is working.

• Rate of Pipe A = 1/1 tank/hour.

• Time required for Pipe A to fill the remaining 1/4 of the tank = Remaining Work / Rate(A) = (1/4) / 1 = 1/4 hours.

• Convert this time back to minutes: (1/4) hours × 60 minutes/hour = 15 minutes.