Question

2 years ago, the average age of a family of 5 members was 18 years. After a new member is added to the family, the average age of the family is still the same. The present age of the newly added member, in years, is:

• A. 8
• B. 6
• C. 10
• D. 5

Answer 1

Answer:

A. 8

Solution:

Given:

The average age of a family of 5 members 2 years ago was 18 years.

The average after a new member add to the family is 18 years.

Concept Used:

The average = Sum of the all numbers/Number of the numbers

Calculation:

The average age of a family of 5 members 2 years ago was 18 years.

The sum of age of all family member 2 years ago $= 18\times{5} = 90$

 

The sum of age of all family member at present $= 90 + 2\times{10} = 100$

Let the age of new member be x.

The sum of age of a family of 6 member $= 6\times{18} = 108$

⇒ 100 + x = 108

⇒ x = 8 years

∴ The age of new member of family is 8 years.

Short Cut:

Let the age of new member be x.

The sum of age of a family of 6 member $= 6\times{18} = 108$

⇒$18\times{5} + 2\times{5} + x = 108$

⇒ 90 + 10 + x = 108

⇒ x = 8 years

∴ The age of new member of family is 8 years.