CAT 2019

Slot 2

QA

Question & Solution

1. Concept Used

• Topic: Ratio, Proportion & Percentage Change
• Formula: $$\text{Percentage Increase} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100$$

2. Calculation

Let the salaries of Ramesh, Ganesh, and Rajesh in 2010 be (6x), (5x), and (7x) respectively, where (x) is a common multiplier.

Let the salaries of Ramesh, Ganesh, and Rajesh in 2015 be (3y), (4y), and (3y) respectively, where (y) is another common multiplier.

We are told that Ramesh's salary increased by 25% from 2010 to 2015. So:

$$3y = 1.25 \times 6x$$

$$3y = 7.5x$$

$$y = 2.5x$$

Now we can find Rajesh's salary in both years:

• Rajesh's salary in 2010 (= 7x)
• Rajesh's salary in 2015 (= 3y = 3 \times 2.5x = 7.5x)

Applying the percentage increase formula:

$$\text{Percentage Increase} = \frac{7.5x - 7x}{7x} \times 100$$

$$= \frac{0.5x}{7x} \times 100$$

$$= \frac{0.5}{7} \times 100$$

$$= \frac{50}{7} \approx 7.14%$$

This is closest to 7%.

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3. Solution

Answer = Option B ✅

The percentage increase in Rajesh's salary during 2010–2015 is approximately 7%.