Question

20 years ago, when my parents got married, their average age was 23 years. Now the average age of my family consisting of myself and my parents only is 35 years. Find out my present age.

Answer 1

Hint: We use the formula of average to find the value of total age. We use that formula for both my parents’ age and all three people. In both cases, we find the total value of their ages. We subtract them at the end to find the solution to the problem.

Complete step-by-step solution:
It's given that 20 years ago when my parents got married, their average age was 23 years.
We know that the average value is found by dividing the total by the number of observations.
Inversely, the total can be found by multiplying the average with the total number of observations.
My parents are two people. The average age of them 20 years ago was 23 years.
So, their total age 20 years ago was $23\times 2=46$ years.
This age has been considered 20 years ago. Now if we need their total age for the present then we are adding 20 years to their ages at that time for both of them.
So basically, we are adding $20\times 2=40$ years in total.
The total age of my parents at the present time is $46+40=86$ years.
It’s also given that the average age of my family consisting of myself and my parents only is 35 years.
Using the average rules, we find that the total age of my family consisting of myself and my parents is $35\times 3=105$ years.
So, we have a total age of three people consisting of myself and my parents as 105 years and the total age of my parents as 86 years.
So, my age will be the difference between these two values.
My age is $105-86=19$ years. So, my present age is 19 years.

Note: We need to remember that we have to convert the average value to the total value. So, the average values will not help in finding the present age. The only case where it will be similar is when the number of observations is the same for both cases.