Question

Mother is 25 year older than her son. Find sons age if after 8 years ratio of sons age to mothers age will be 4÷ 9

Answer 1

Let son's age be x

So mother's age will be 25 + x


After 8 years, son's age = x + 8

Mother's age = 25 + x + 8

=> Mother's age = 33 + x

Given that their ratio is 4/9

=> (x + 8)/(33 + x) = 4/9

Cross multiply them

=> 9(x + 8) = 4(33 + x)

=> 9x + 72 = 132 + 4x

=> 9x - 4x = 132 - 72

=> 5x = 60

=> x = 60/5

=> x = 12 years.

So, son's age = x = 12 years.

Mother's age = x + 25 = 12 + 25 = 37 years.

Answer 2

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Let son's age be p

So mother's age will be 25 + p

Son's age After 8 years = p + 8

Mother's age = 25 + p + 8

=> Mother's age = 33 + p

Given that their ratio is $\bf\huge\frac{4}{9}$

=> $\bf\huge\frac{p\: +\: 8}{33\:+\:p} = \frac{4}{9}$

Multiply :-

=> 9(p + 8) = 4(33 + p)

=> 9p + 72 = 132 + 4p

=> 9p - 4p = 132 - 72

=> 5p = 60

=> p = $\bf\huge\frac{60}{5}$

=> p = 12 years.

Son's age = 12 years.

Mother's age = p + 25

= 12 + 25

= 37 years.

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