A cistern is filled by Pipe A and Pipe B together in 2.4 hours. Pipe A alone can fill the cistern at the rate

Question

A cistern is filled by Pipe A and Pipe B together in 2.4 hours. Pipe A alone can fill the cistern at the rate of 100 litres per hour. Pipe B alone can fill the cistern in 4 hours. What is the capacity of the cistern?

Examoogle · Accepted Answer

The correct answer is Option B: 600 litres. Calculate Pipe A's share of total capacity per hour relative to Pipe B, or use the relationship: Total Capacity = (Rate of A + Rate of B) × Time_combined, where Rate_B = Total Capacity / 4.

Step-by-Step Solution & Concepts:
Shortcut Trick: Calculate Pipe A's share of total capacity per hour relative to Pipe B, or use the relationship: Total Capacity = (Rate of A + Rate of B) × Time_combined, where Rate_B = Total Capacity / 4.

Formula Used: $$\frac{1}{A} + \frac{1}{B} = \frac{1}{T_{combined}}$$

Given: Time taken by Pipe A and B together = 2.4 hours. Rate of Pipe A = 100 litres per hour. Time taken by Pipe B alone = 4 hours.

Steps: Define Rates: Let the total capacity be $C$. The rate of pipe $A$ is given as $100$ L/hr. The rate of pipe $B$ is $\frac{C}{4}$ L/hr.. Combined Rate Equation: The cistern is filled together in $2.4$ hours. Therefore, the combined rate is the total capacity divided by the time.. Solve for C: Substitute the rates into the equation: $100 + \frac{C}{4} = \frac{C}{2.4}$. Rearranging gives $100 = C(\frac{1}{2.4} - \frac{1}{4})$. Calculating the difference: $\frac{1}{2.4} - \frac{1}{4} = \frac{4 - 2.4}{9.6} = \frac{1.6}{9.6} = \frac{1}{6}$.

Answer: B is correct because the calculated capacity of the cistern is 600 litres.

Exam Tip: This concept of 'Rate = Work/Time' is identical to solving speed-distance-time problems where Rate is speed and Work is total distance.

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