CAT 2025 Slot 3 QA Question 13

Multiple choice (+3 / −1) · Arithmetic · Time & Work · Try it, then check the answer and solution below.

CAT 2025 Slot 3QAArithmetic • Time & WorkModerate

The rate of water flow through three pipes A, B and C are in the ratio 4 : 9 :

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

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Official Convenor Answer Key: C

Answer and solution

Answer: C) 73

📌 Core Concept

The rates of work (filling the tank) of pipes A, B, and C are given in the ratio 4:9:36. The combined work rate when all pipes are open is the sum of their individual rates. The time taken to fill the tank is the reciprocal of the combined work rate.

🔢 Step-by-Step Solution

Determine Individual Rates:

Let the rates be

4x , 9x , and

36x$ for pipes A, B, and C respectively.

Given pipe A fills the tank in 15 hours, its rate is

\frac{1}{15}

$ per hour.

Therefore,

4x = \frac{1}{15}

⇒

x = \frac{1}{60}

Calculate Each Pipe's Rate:

Pipe A:

4x = \frac{4}{60} = \frac{1}{15}

per hour.

Pipe B:

9x = \frac{9}{60} = \frac{3}{20}

per hour.

Pipe C:

36x = \frac{36}{60} = \frac{3}{5}

per hour.

Combine the Rates:

Total rate =

\frac{1}{15}

\frac{3}{20}

\frac{3}{5}

Convert to a common denominator (60):

\frac{4}{60} + \frac{9}{60} + \frac{36}{60} = \frac{49}{60}

per hour.

Calculate Time to Fill the Tank:

Time = \frac{1}{\text{Total Rate}} = \frac{1}{

\frac{49}{60}

} =

\frac{60}{49}

hours.

Convert hours to minutes: \( \frac{60

CAT 2025 Slot 3 QA Question 13

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