Question

Two pipes A and B together can fill a tank in 40 minutes. Pipe A is twice as fast as pipe B. Pipe A alone can fill the tank in:

• A. 1 hour
• B. 2 hours
• C. 80 minutes
• D. 20 minutes

Answer 1

The Correct Option is A

Let the time taken by pipe \( B \) alone to fill the tank be \( x \) minutes. Since pipe \( A \) is twice as fast as pipe \( B \), the time taken by pipe \( A \) to fill the tank alone is \( \frac{x}{2} \) minutes.

The combined rate of pipes \( A \) and \( B \) is:  
\(\frac{1}{x} + \frac{2}{x} = \frac{3}{x}.\)

The two pipes together can fill the tank in 40 minutes, so their combined rate is:  \(\frac{1}{40}.\)

Equating the rates:  
\(\frac{3}{x} = \frac{1}{40}.\)

Solve for \( x \):  
\(x = 120 \ \text{minutes}.\)

Thus, pipe \( A \) alone can fill the tank in:  
\(\frac{x}{2} = \frac{120}{2} = 60 \ \text{minutes} = 1 \ \text{hour}.\)