Question

The age of the boy is one-fifth of the age of his mother and sum of the ages of the son and the mother is equal to the age of the father. After 15 years, the sum of the ages of the son and his mother will be four-third of his father’s age. Find the ratio of the present age of son, mother and father

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Answer 1

$\\ \\ \: \large\rm \color{navy} \underline{ \: Question :- }$

The age of the boy is one-fifth of the age of his mother and sum of the ages of the son and the mother is equal to the age of the father. After 15 years, the sum of the ages of the son and his mother will be four-third of his father’s age. Find the ratio of the present age of son, mother and father.

$\\ \\ \: \large\rm \color{navy} \underline{ \: Answer :- }$

$\\ \: \: \sf \: \: \: \: \: \: \: \: \: \: \longrightarrow \: 1 \: : \: 5 \: : \: 6$

$\\ \\ \: \large\rm \color{navy} \underline{ \: Solution :- }$

$\\ \sf \: Let \: the \: present \: age \: of \: the \: son \: be \red{ \bold {\: x}} ,$

$\\ \: \sf \: \: \: \: \: \: \: \: \: \: \: So, \: the \: age \: of \: his \: mother \: = \red{\bold{ 5x}} \:$

$\\ \sf \: \: \: \: Now , \: the \: father's \: age \:= \: age \:of \: mother \:+ \:age \:of \:son \\ \: \: \: \: \: \: \: = \sf \: 5x + x \\ = \red {\bold {{6x}}}$

$\\ \sf \: \: \: \: So,\: the \: ratio\:of\:there\:ages\: = son's\:age \: : \: mother's\:age \: : \: father's\:age\:$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies\: \: x \: : \: 5x \: : \: 6x$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies\pink {\underline {\boxed{{ \frak{\: 1\: : \: 5 \: : \: 6}}} }}$

Answer 2

Given:

✰ The age of the boy is one-fifth of the age of his mother.

✰ Sum of the ages of the son and the mother is equal to the age of the father.

To find:

✠ The ratio of the present age of son, mother and father.

Solution:

❀ Here in this question we have to frame the equation by using the data which is given to us and find the ratio between their ages. After 15 years, the sum of the ages of the son and his mother will be four-third of his father’s age - this is just given to confuse us Here we just have to find their present ages that's why we will use what is given first to us and find the ratio between the ages.

Let the age of son be x.

Now, we know that the age of boy i.e., son is one-fifth of the age of his mother, so

• Age of boy = 1/5 × age of mother
• x = 1/5 × age of mother
• Age of mother = 5x

Now, we know that the sum of the ages of the son and the mother is equal to the age of the father.

• Age of father = Age of son + Age of mother
• Age of father = x + 5x
• Age of father = 6x

So, the ratio of their ages = x : 5x : 6x

The ratio of their ages = 1 : 5 : 6

∴ The ratio of the present age of son, mother and father = 1 : 5 : 6

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