CAT 2017

Slot 1

QA

Question & Solution

1. Concept Used

• Topic: Percentage, Linear Equations in Age Problems
• Formula: $$\text{Percentage Increase} = \frac{\text{Increase in Age}}{\text{Original Age}} \times 100$$

2. Calculation

Let Arun's current age be ( A ) years. Since Arun's age is 40% of Barun's current age, we have:

$$A = 0.4 \times B \implies B = \frac{A}{0.4} = 2.5A$$

So Barun's current age is ( 2.5A ).

Now, let ( X ) be the number of years after which Arun's age becomes half of Barun's age. At that point:

$$A + X = \frac{1}{2}(2.5A + X)$$

Multiplying both sides by 2:

$$2(A + X) = 2.5A + X$$

$$2A + 2X = 2.5A + X$$

$$2X - X = 2.5A - 2A$$

$$X = 0.5A$$

So after ( X = 0.5A ) years, Barun's age increases from ( 2.5A ) to ( 2.5A + 0.5A = 3A ).

The percentage increase in Barun's age is:

$$\text{Percentage Increase} = \frac{0.5A}{2.5A} \times 100 = \frac{0.5}{2.5} \times 100 = 0.2 \times 100 = 20%$$

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3. Solution

Answer = 20 ✅

Barun's age will increase by 20% during this period.