Question

A child's age is 2/3 of his elder brother after 5 years, he will be fourth-fifth of the elder brother's age . How old is the child?

Answer 1

Answer:

The answer is 5 years

Step-by-step explanation:

Let the present age of child be x and that of elder brother be y.

After 5 years: age of child and brother will be X+5 and Y+5 respectively.

$X = \frac{2}{3} Y --- (1) X+5= \frac{4(Y+5)}{5}  5X + 25 = 4 Y + 20 5X-4Y = -5 -----(2)On solving 1 and 2 , we get \\X= 5 years$

Answer 2

Answer:

The child would be 5 years old.

Step-by-step explanation:

Let x be the age of the elder brother,

So, the age of the child = $\frac{2x}{3}$

After 5 years,

The age of elder brother = x + 5,

While, the age of child = $\frac{2x}{3}+5$

According to the question,

$\frac{2x}{3}+5 = \frac{4}{5}(x+5)$

$\frac{2x+15}{3}=\frac{4x+20}{5}$

$10x + 75 = 12x+60$

$75-60 = 12x - 10x$

$15 = 2x$

$\implies x = \frac{15}{2}$

Hence, the age of child = $\frac{2}{3}\times \frac{15}{2}=5$

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