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

Answer:

1:5:6

Solution :

Frame the equation using the given data and get the relation among son's age, mother's age and father's age. For example, if son's age=x years, mother's age is 5x years and father's age is 6x years.

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 = age of the father.
• And after 15 years, the sum of the ages of the son and his mother will be four-third of his father’s age.

To Find:-

• the ratio of the present age of son, mother and father.

Solution:-

Let's assume that the age of son is x years.

Now,

[ First scenario:- ]

Age of son is equal to the 1/5th of the age of his mother.

Age of son = 1 / 5 ( age of mother )

x = 1 / 5 × age of mother

Age of mother = 5x

Therefore, age of mother is 5x.

[ Second scenario:- ]

As it is given that sum of the ages of the son and the mother is equal to the age of the father.

Father's age = age of son + age of mother

Father's age = x + 5x

Father's age = 6x

Therefore, age of father is 6x.

★ Ratio of present age of son, mother and father will be equal to:-

= x : 5x : 6x

= 1 : 5 : 6

Hence, the ratio of the present age of son, mother and father is 1 : 5 : 6.