Question

Mother is 25 year older than her son. Find son's age if after 8 years ratio of son's age to mother's age will be 4/9​

Answer 1

ANSWER

Let the son's age be denoted as x.

Given

Mother is 25 years older than her son.

∴ The mother's age = x + 25

8 years later, the ratio of the son's age to the mother's age will be 4/9.

$\implies \dfrac{x+8}{x+25+8} = \dfrac{4}{9\\}$

$\implies \dfrac{x+8}{x+33} = \dfrac{4}{9}$

$\implies 9(x+8)=4(x+33)$

$\implies 9x+72=4x+132$

$\implies 9x-4x=132-72$

$\implies 5x=60$

$\implies \underline{\underline{x=12}}}$

$\boxed{\boxed{\bold{Therefore, \ the \ son's \ age \ is \ 12 \ years.}}}}}$

                                                     

Answer 2

Answer:

Given :-

• Mother is 25 year older than her son.
• After 8 years ratio of son's age to mother's age will be 4/9.

To Find :-

• What is the son's age.

Solution :-

Let,

$\mapsto \bf Present\: Age_{(Son)} =\: a\: years$

$\mapsto \bf Present\: Age_{(Mother)} =\: (a + 25)\: years$

★ After 8 years :

$\leadsto \sf Age_{(Son)} =\: (a + 8)\: years$

$\leadsto \sf Age_{(Mother)} =\: (a + 25 + 8)\: years$

According to the question :

$\clubsuit$ The ratio of son's age to mother's age will be 4/9.

So,

$\implies \bf \bigg\{\dfrac{Age_{(Son)}}{Age_{(Mother)}}\bigg\} =\: \bigg\{\dfrac{4}{9}\bigg\}$

$\implies \sf \dfrac{a + 8}{a + 25 + 8} =\: \dfrac{4}{9}$

$\implies \sf \dfrac{a + 8}{a + 33} =\: \dfrac{4}{9}$

By doing cross multiplication we get,

$\implies \sf 4(a + 33) =\: 9(a + 8)$

$\implies \sf 4a + 132 =\: 9a + 72$

$\implies \sf 4a - 9a =\: 72 - 132$

$\implies \sf {\cancel{-}} 5a =\: {\cancel{-}} 60$

$\implies \sf 5a =\: 60$

$\implies \sf a =\: \dfrac{\cancel{60}}{\cancel{5}}$

$\implies \sf a =\: \dfrac{12}{1}$

$\implies \sf\bold{\purple{a =\: 12}}$

Hence, the required present ages of son and mother is :

☆ Present Age Of Son :

$\dashrightarrow \sf Present\: Age_{(Son)} =\: a\: years$

$\dashrightarrow \sf\bold{\red{Present\: Age_{(Son)} =\: 12\: years}}$

☆ Present Age Of Mother :

$\dashrightarrow \sf Present\: Age_{(Mother)} =\: (a + 25)\: years$

$\dashrightarrow \sf Present\: Age_{(Mother)} =\: (12 + 25)\: years$

$\dashrightarrow \sf\bold{\red{Present\: Age_{(Mother)} =\: 37\: years}}$

$\therefore$ The son's age is 12 years .