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. 20
• B. 25
• C. 30
• D. 40

Hint:

When solving age problems with percentages, it is often easiest to assume a base value like 100 for one of the people to make the calculations concrete.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept: 
This is a problem involving ratios and linear aging. As years pass, the same number of years is added to both individuals' ages. 
Step 2: Key Formula or Approach: 
Let Barun's current age be \( B \) and Arun's be \( A \).
Currently: \( A = 0.4B \).
After \( n \) years: \( A + n = 0.5(B + n) \). 
Step 3: Detailed Explanation: 
Substitute \( A = 0.4B \) into the second equation: \[ 0.4B + n = 0.5B + 0.5n \] \[ n - 0.5n = 0.5B - 0.4B \] \[ 0.5n = 0.1B \] \[ n = \frac{0.1}{0.5}B = \frac{1}{5}B = 0.2B \] The question asks by what percentage Barun's age will increase. Barun's age increases by \( n \) years.
Percentage increase: \[ \left( \frac{n}{B} \right) \times 100 = \left( \frac{0.2B}{B} \right) \times 100 = 20\% \] Wait, let's re-verify the logic.
Initial: \( A=40, B=100 \).
After \( n \) years: \( 40+n = 0.5(100+n) \implies 40+n = 50+0.5n \implies 0.5n = 10 \implies n=20 \).
Barun's new age = 120.
Increase = 20.
Percentage increase = \( (20/100) \times 100 = 20\% \).
Note: If the options provided don't match exactly or imply a different perspective, let's check the ratio shift.
If Barun's age was 100 and becomes 125 (a 25% increase), his age is 125. Arun's would be \( 40+25=65 \). \( 65/125 = 0.52 \). (No)
If increase is 20\%: Barun is 120, Arun is 60. \( 60/120 = 0.5 \). (Yes, this matches the condition).
The correct mathematical answer is 20. If 20 is option (a), that is the answer. 
Step 4: Final Answer: 
Barun's age will increase by 20%.