Question

Two pipes A and B can fill a tank in 5 hours and 20 hours respectively. Both pipes together can fill the same tank in:

• A. 4 hours
• B. 6 hours
• C. 10 hours
• D. 2 hours

Answer 1

The Correct Option is A

To determine how long it will take for both pipes A and B to fill the tank together, we need to first establish how much of the tank each pipe fills in one hour. This approach is based on the concept of rate of work.

Step 1: Determine the individual rates of pipes A and B.

• Pipe A can fill the tank in 5 hours. Therefore, in one hour, pipe A fills \frac{1}{5} of the tank.
• Pipe B can fill the tank in 20 hours. Therefore, in one hour, pipe B fills \frac{1}{20} of the tank.

Step 2: Calculate the combined rate of both pipes operating together.

• The combined rate of the pipes is the sum of their individual rates: \frac{1}{5} + \frac{1}{20}.
• To add these fractions, find a common denominator. The least common multiple of 5 and 20 is 20.
• Convert \frac{1}{5} to \frac{4}{20}.
• Now add: \frac{4}{20} + \frac{1}{20} = \frac{5}{20} = \frac{1}{4}.

Step 3: Determine the time taken by both pipes together to fill the tank.

• If together they fill \frac{1}{4} of the tank in one hour, they will fill the entire tank in 4 hours.

Conclusion: Both pipes A and B together can fill the tank in 4 hours. Thus, the correct option is 4 hours.