CAT 2023 Slot 1 QA Question 13

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

CAT 2023 Slot 1QAArithmetic • Ratio, Proportion & VariationEasy

The salaries of three friends Sita, Gita and Mita are initially in the ratio $5 : 6 : 7 , respectively. In the first year, they get salary hikes of

20\% , 25\%

and

20\% , respectively. In the second year, Sita and Mita get salary hikes of

40\%

and

25\% , respectively, and the salary of Gita becomes equal to the mean salary of the three friends. The salary hike of Gita in the second year is

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Official Convenor Answer Key: A

Answer and solution

Answer: A) $26\%$

📌 Core Concept

The problem involves understanding ratios, percentage increases, and mean calculations. The key formula used is the percentage increase formula:

\text{New Salary} = \text{Original Salary} \times (1 + \frac{\text{Percentage Increase}}{100})

🔢 Step-by-Step Solution

Initial Salaries:

Let the initial salaries be

5x , 6x , and

7x$ for Sita, Gita, and Mita respectively.

First Year Hikes:

Sita:

5x \times 1.20 = 6x

Gita:

6x \times 1.25 = 7.5x

Mita:

7x \times 1.20 = 8.4x

Second Year Hikes:

Sita:

6x \times 1.40 = 8.4x

Mita:

8.4x \times 1.25 = 10.5x

Gita:

7.5x \times (1 + \frac{y}{100})

Mean Salary Calculation:

Mean = \frac{8.4x + 10.5x + 7.5x(1 +

\frac{y}{100}

)}{3}$

Equation Setup:

7.5x(1 + \frac{y}{100}) = \frac{8.4x + 10.5x + 7.5x(1 + \frac{y}{100})}{3}

Solving for

y

Multiply both sides by 3: \(22.5x(1 +

\frac{y}{100}

$) = 18.9x + 7.5x(1 + \frac{y}{1

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