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?

Entered answer:

✅ Correct Answer: 20

We have two people with changing age ratios:

Currently: Arun's age = 40% of Barun's age

In the future: Arun's age = 50% of Barun's age

We need to find: How much will Barun's age increase (as a percentage)?

The crucial concept that makes this problem easy: The difference between two people's ages never changes.

If Barun is 5 years older than Arun today, he'll still be 5 years older after 10 years, 20 years, or any number of years!

Let's say Barun's current age = 10x years

Since Arun's age is 40% of Barun's:

Arun's current age = 40% of 10x = 4x years

Age difference = 10x - 4x = 6x years

In the future, when Arun's age becomes 50% of Barun's age:

Let Barun's future age = B years

Then Arun's future age = 50% of B = 0.5B years

Since the age difference remains the same:

B - 0.5B = 6x

0.5B = 6x

B = 12x

So Barun's future age = 12x years

Increase in Barun's age = 12x - 10x = 2x years

Percentage increase = $\tfrac{\text{Increase}}{\text{Original}} \times 100\%$

Percentage increase = $\tfrac{2x}{10x} \times 100\% = \tfrac{2}{10} \times 100\% = 20\%$

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

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Arun's present age in years is 40%40\%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?

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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?