Question

A cistern is filled in 30 minutes by three pipes A, B and C. The pipe C is thrice as fast as pipe A and pipe B is twice as fast as A. The time taken by pipe A alone to fill the cistern is:

• A. 180 minutes
• B. 270 minutes
• C. 300 minutes
• D. 250 minutes

Answer 1

The Correct Option is A

Let's solve the problem by analyzing the filling rates of each pipe. Let the rate at which pipe A fills the cistern be \( x \). Hence,

Rate of pipe A = \( x \)

Rate of pipe B = \( 2x \)

Rate of pipe C = \( 3x \)

The combined rate of all three pipes is \( x + 2x + 3x = 6x \).

According to the problem, the cistern is filled in 30 minutes by all three together. Thus, the equation for the filling rate is given by:

\[\text{Time} \times \text{Rate} = \text{Full Work}\]

\[30 \times 6x = 1\]

\[180x = 1\]

\[x = \frac{1}{180}\]

The rate of pipe A is \( x = \frac{1}{180} \). Therefore, the time taken by pipe A alone to fill the cistern is the reciprocal of its rate:

\[\text{Time by A alone} = \frac{1}{x} = 180 \text{ minutes}\]

Therefore, the time taken by pipe A to fill the cistern alone is 180 minutes.