Question

Arun's present age in years is 40% of Barun's. In another few years, Arun's age will be half of Barun's. By what percentage will Barun's age increase during this period?

• A. 26
• B. 18
• C. 20
• D. 23

Answer 1

The Correct Option is C

Step 1: Define variables

Let Barun’s present age be: \[ B = 10x \] Let Arun’s present age be: \[ A = 4x \] The difference in their ages is: \[ B - A = 10x - 4x = 6x \] This difference \( 6x \) is constant over time.

Step 2: When Arun’s age is 50% of Barun’s age

We are told that at some point in the future, Arun’s age will be half of Barun’s age: \[ A' = 0.5 \times B' \] At that stage, the age difference will still be \( 6x \), but now it is also half of Barun’s age: \[ B' - A' = 0.5B' \] Substitute \( B' - A' = 6x \): \[ 6x = 0.5B' \quad\Rightarrow\quad B' = 12x \]

Step 3: Change in Barun’s age

Barun’s present age is \( 10x \) and at that future moment it will be \( 12x \). The increase is: \[ 12x - 10x = 2x \] The percentage increase in Barun’s age is: \[ \frac{2x}{10x} \times 100\% = 20\% \]

Final Answer:

Barun’s age increases by: \[ \boxed{20\%} \]