The Average Age of a Family of 5 Members is 20 Years GMAT Problem Solving

Question: The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member?

  1. 9.5
  2. 10.5
  3. 11.5
  4. 12.5
  5. 13.5

Correct Answer: D

Solution and Explanation:
Approach Solution 1:

The details that are given in the above-mentioned question are;
Average age of the family members= 20 years
Age of the youngest member of the family= 10 years
The formula to calculate the average of anything is mentioned below:
Sum of the total items given/ number of items.

Thus, in this case the formula becomes;
Sum of the age of the family members/ total number of members.

Mentioned below is the calculation approach for the given question:
Firstly we are required to calculate the total age of the members. In order to do this, we need to multiply 5 by 20.

This implies; 5 * 20= 100.

However, considering the age of the newborn being 0.

The age of each of the family members can be calculated by subtracting the age of the newborn at present from the total age of the family members. Therefore; 100 - 10= 90.
This implies that the average age of 4 members is = 90 ÷ 4= 22.5
However, considering the newborn that didn’t exist 10 years ago, the average age will be
= 22.5 – 10 = 12.5.

Therefore, the average age of the family at the time of the birth of the youngest member = 12.5 years.

Approach Solution 2:
The problem statement states that:
Given: 

  • The average age of a family of 5 members is 20 years.
  • The age of the youngest member is 10 years. 

Find Out:

  • The average age of the family at the time of the birth of the youngest member.

Total age of the family = 20*5 = 100
The age of the youngest member is 10 years

We have to find the average of the family when the youngest member was born.
Therefore, the total age of the family when the youngest member was born = 100 - 10*5 = 50.

Since the youngest member is not there 10 years ago, then the members are 4.
Average age = 50/4 = 12.5

Therefore, the average age of the family at the time of the birth of the youngest member = 12.5 years

Approach Solution 3:
The problem statement informs that:
Given: 

  • The average age of a family of 5 members is 20 years.
  • The age of the youngest member is 10 years. 

Find Out:

  • The average age of the family at the time of the birth of the youngest member.

Let the average age of the family at the time of the birth of the youngest member is x.

Then, the total age of the family at the time of the birth of the youngest member is 4x.

After 10 years, the total age will increase by 10 * 4 = 40 years.
Hence, the total current age of the 4 persons will be = 4x + 40 years.

The youngest member of the family is 10 years old.
Hence, the total age of all the 5 members will be = 4x + 40 + 10 = 4x + 50

Therefore, the average age of all the 5 members will be = (4x + 50)/5

As per the question:
The average age of a family of 5 members is 20 years
Therefore, we can say:
(4x + 50)/5 = 20
=> 4x + 50 = 100
=> 4x = 50
=> x = 50/4
=> x = 12.5

Therefore, the average age of the family at the time of the birth of the youngest member = 12.5 years

“The average age of a family of 5 members is 20 years” - is a topic of the GMAT Quantitative reasoning section of the GMAT exam. To solve the GMAT Problem Solving questions, the candidates must have a solid understanding of calculation and mathematics. The candidates can practise varieties of questions from GMAT Quant practice papers that will enable them to improve their mathematical skills.

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