CAT 2024 Slot 1 QA Question 11

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

CAT 2024 Slot 1QAArithmetic • Mixture & AlligationEasy

A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process of pouring out two-thirds the content and replacing with water is repeated three more times, then the final ratio of milk to water in the glass, is

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Official Convenor Answer Key: B

Verified Solution:

### Core Concept The problem involves repeated dilution where a fraction of the mixture is replaced with water. The formula to determine the remaining concentration of the original substance after each replacement is:

\text{Remaining concentration} = \left(1 - \frac{\text{Fraction replaced}}{}\right)^{\text{Number of replacements}}

### Step-by-Step Solution

Initial Setup: The glass is initially filled with milk. Let the initial volume be

V

First Replacement: Two-thirds of the milk is poured out, leaving one-third. The remaining milk is

\frac{1}{3}

V$.

Subsequent Replacements: This process is repeated three more times. Each time, the remaining milk is multiplied by

\frac{1}{3}

Final Concentration: After four replacements, the remaining milk is:

\left(\frac{1}{3}\right)^4 V = \frac{1}{81}V

Ratio Calculation: The ratio of milk to water is:

\frac{\frac{1}{81}V}{\frac{80}{81}V} = 1 : 80

### 30-Second Shortcut Each replacement retains

\frac{1}{3}

of the milk. After four replacements, the milk fraction is \left(\frac{1}{3}\right)^4 = \frac{1}{81}

. Thus, the ratio is

1 : 80

### Final Answer Confirmation Correct Answer: B

Answer and solution

Answer: B) 1 : 80

\text{Remaining concentration} = \left(1 - \frac{\text{Fraction replaced}}{}\right)^{\text{Number of replacements}}

### Step-by-Step Solution

Initial Setup: The glass is initially filled with milk. Let the initial volume be

V

First Replacement: Two-thirds of the milk is poured out, leaving one-third. The remaining milk is

\frac{1}{3}

V$.

Subsequent Replacements: This process is repeated three more times. Each time, the remaining milk is multiplied by

\frac{1}{3}

Final Concentration: After four replacements, the remaining milk is:

\left(\frac{1}{3}\right)^4 V = \frac{1}{81}V

Ratio Calculation: The ratio of milk to water is:

\frac{\frac{1}{81}V}{\frac{80}{81}V} = 1 : 80

### 30-Second Shortcut Each replacement retains

\frac{1}{3}

of the milk. After four replacements, the milk fraction is \left(\frac{1}{3}\right)^4 = \frac{1}{81}

. Thus, the ratio is

1 : 80

### Final Answer Confirmation Correct Answer: B

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