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

Answer 1

we can assume that

Age of Arun = A and age of Barun = B

Let us assume, A=0.4 B —– (1)

After a few years, A+x = 0.5(B+x) —– (2)

On putting value of A in eq (2), we get x = 0.2B

% increase in the age of B = (0.2B/B) *100 = 20%

Answer: 20%

Answer 2

Barun's age will increase during the period by 20%

Given :

• Arun's present age in years is 40% of Barun's

• In another few years, Arun's age will be half of Barun's

To find :

The percentage Barun's age will increase during this period

Solution :

Step 1 of 2 :

Form the equation to find the time period

Let Barun's present age = 100x years

Since Arun's present age in years is 40% of Barun's

∴ Arun's present age = 40x years

Let after t years, Arun's age will be half of Barun's

After t years,

Arun's age will be = (40x + t) years

Barun's age will be = (100x + t) years

By the given condition

$\displaystyle \sf (40x + t) = \frac{1}{2} (100x + t)$

Step 2 of 2 :

Calculate the percentage of Barun's age increase during this period

$\displaystyle \sf (40x + t) = \frac{1}{2} (100x + t)$

$\displaystyle \sf{ \implies }(100x + t) = 2(40x + t)$

$\displaystyle \sf{ \implies }100x + t = 80x + 2t$

$\displaystyle \sf{ \implies }2t - t = 100x - 80x$

$\displaystyle \sf{ \implies }t = 20x$

So after 20x years, Arun's age will be half of Barun's

Barun's present age = 100x years

After 20x years,

Barun's age will be

= (100x + 20x) years

= 120x years

∴ Barun's age increase during this period = 20x years

Hence percentage Barun's age will increase during this period

$\displaystyle \sf = \frac{20x}{100x} \times 100\%$

$\displaystyle \sf = \frac{20}{100} \times 100\%$

$\displaystyle \sf = 20\%$

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