Question

A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?

Answer 1

Hint: We are given the average age of some members of a family. We need to be aware about some basic rules of averages. Here, we are given the average age of n number of groups, so we simply will multiply each average with the given number of members present in that group so that we are able to find the total sum of all the ages. After that we will multiply the sum of ages by the total number of members in the family. And in this way we will obtain the average age of the family.

Complete step-by-step answer:
We will look at the average age one by one and then to calculate the total sum of the ages, we will multiply the average age with the number of members present of that age. There are two grandparents with an average age of 67. So, the sum of ages of two grandparents is:
$S_1=67\times 2=134$
Next, there are two parents with average age 35, so the sum of ages of the parents is:
$S_2=35\times 2=70$
Finally, there are three grandchildren with an average age of 6, so the sum of ages of the grandchildren is:
$S_3=6\times 3=18$
The total number of members in the family is:
$n=2+2+3=7$
So, the average age of the family is:
$\text{Average age}=\dfrac{S_1+S_2+S_3}{n}=\dfrac{134+70+18}{7}=\dfrac{222}{7}=31\dfrac{5}{7}\text{years}$
Hence, the average age has been found out.

Note: If you are strong with calculation, there is no need to find out separately each sum of the different groups, you can simply multiply the average age directly with the number of members and add them together. Also make sure that you do as few calculation mistakes as possible.