CAT 2025

Slot 3

QA

Question & SolutionQues & Sol

The rate of water flow through three pipes A, B and C are in the ratio 4 : 9 : 36. An empty tank can be filled up completely by pipe A in 15 hours. If all the three pipes are used simultaneously to fill up this empty tank, the time, in minutes, required to fill up the entire tank completely is nearest to

1. Concept Used

• Topic: Pipes and Cisterns (Time, Speed and Distance)
• Formula: $ \text{Time to fill} = \frac{\text{Capacity of Tank}}{\text{Combined Rate of All Pipes}} $

2. Calculation

Let the rates of flow of pipes A, B, and C be $4x$, $9x$, and $36x$ units per hour respectively, consistent with the given ratio $4 : 9 : 36$.

Since pipe A alone fills the tank in 15 hours, the total capacity of the tank is: $\text{Capacity} = \text{Rate of A} \times \text{Time} = 4x \times 15 = 60x \text{ units}$

When all three pipes work simultaneously, their combined rate of flow is: $\text{Combined Rate} = 4x + 9x + 36x = 49x \text{ units per hour}$

The time required to fill the tank when all three pipes work together is: $\text{Time} = \frac{60x}{49x} = \frac{60}{49} \text{ hours}$

Converting this to minutes by multiplying by 60: $\text{Time in minutes} = \frac{60}{49} \times 60 = \frac{3600}{49} \approx 73.47 \text{ minutes}$

Among the given options — 73, 78, 76, and 71 — the value 73 is the closest to 73.47.

3. Solution

Answer = Option A ✅

The final calculated value is approximately 73.47 minutes, and the nearest answer is 73.