Question

My mother is three times older than the age of my sister. My father is thirty years older than me. I was five years old when my sister born, if my sister is 16 years old The difference in the age of my parents is

Answer 1

Hint: This is an age-based question. In this question there are four members of the family given, these members are – a brother, a sister, mother and father. We have to find the difference between the age of the parents. By using the age relations given in the question we can solve this question.

Complete step-by-step answer:
Given:
Let us assume the present age of the sister is $ x $ years.
Then according to the question, the age of a mother is three times than the age of sister.
So, the age of mother $ = 3x $
Now according to the question, the sister was born when the brother was five years old.
So, the age of brother $ = x + 5 $
Also, the age of the father is 30 years greater than the age of brother.
So, the age of father
$
 = x + 5 + 30\\
 = x + 35
 $
Also, we have given,
The age of sister $ x = 16{\rm{ years}} $
Then the difference between the age of parents $ = $ the age of father $ - $ the age of mother
Substituting the values, we get,
The difference between the age of parents
$
 = \left( {x + 35} \right) - 3x\\
 = 35 - 2x
 $
Substituting $ x = 16 $ we get,
The difference between the age of parents
$
 = 35 - 2 \times 16\\
 = 35 - 32\\
 = 3{\rm{ years}}
 $
Therefore, the difference in the age of parents is 3 years.

Note: The alternate method of solving this question is that in the question all the values of the age given are in relation with each other so we can assume a variable for the age for example x or y, and then form the equations in terms of the age variable. By solving this equation, we can find the age of the family members required and then the difference between the parents age can be calculated.