CAT 2025 Slot 2 QA Question 6

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

CAT 2025 Slot 2QAArithmetic • Ratio, Proportion & VariationModerate

The ratio of expenditures of Lakshmi and Meenakshi is

2:3 , and the ratio of income of Lakshmi to expenditure of Meenakshi is

6:7

. If excess of income over expenditure is saved by Lakshmi and Meenakshi, and the ratio of their savings is

4:9 , then the ratio of their incomes is

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Official Convenor Answer Key: C

Verified Solution:

### Core Concept The problem involves ratios of expenditures, income, and savings. We use the concept of ratios and algebraic manipulation to find the required ratio of incomes.

### Step-by-Step Solution

Let the expenditures be:

Lakshmi:

2k

Meenakshi:

3k

From the given ratio:

\frac{I_L}{E_M} = \frac{6}{7}

I_L = \frac{6}{7} \times 3k = \frac{18k}{7}

Calculate Lakshmi's savings:

Savings

S_L = I_L - E_L = \frac{18k}{7} - 2k = \frac{18k - 14k}{7} = \frac{4k}{7}

Given savings ratio:

\frac{S_L}{S_M} = \frac{4}{9}

\frac{4k/7}{S_M} = \frac{4}{9} \Rightarrow S_M = \frac{9k}{7}

Calculate Meenakshi's income:

S_M = I_M - E_M \Rightarrow \frac{9k}{7} = I_M - 3k

I_M = 3k + \frac{9k}{7} = \frac{21k + 9k}{7} = \frac{30k}{7}

Find the ratio of incomes:

\( I_L : I_M =

\frac{18k}{7}

:

\frac{30k}{7}

= 18 : 3

Answer and solution

Answer: C) 3 : 5

### Core Concept The problem involves ratios of expenditures, income, and savings. We use the concept of ratios and algebraic manipulation to find the required ratio of incomes.

### Step-by-Step Solution

Let the expenditures be:

Lakshmi:

2k

Meenakshi:

3k

From the given ratio:

\frac{I_L}{E_M} = \frac{6}{7}

I_L = \frac{6}{7} \times 3k = \frac{18k}{7}

Calculate Lakshmi's savings:

Savings

S_L = I_L - E_L = \frac{18k}{7} - 2k = \frac{18k - 14k}{7} = \frac{4k}{7}

Given savings ratio:

\frac{S_L}{S_M} = \frac{4}{9}

\frac{4k/7}{S_M} = \frac{4}{9} \Rightarrow S_M = \frac{9k}{7}

Calculate Meenakshi's income:

S_M = I_M - E_M \Rightarrow \frac{9k}{7} = I_M - 3k

I_M = 3k + \frac{9k}{7} = \frac{21k + 9k}{7} = \frac{30k}{7}

Find the ratio of incomes:

\( I_L : I_M =

\frac{18k}{7}

:

\frac{30k}{7}

= 18 : 3

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