Question

The average age of 4 members of a family is 25 years if the age of head of family is also included in the average age is increased by 20% what is the age of the head of the family

Answer 1

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Answer 2

The age of head of the family is 50

Step-by-step explanation:

The average age of 4 members of a family is 25 years

$Average = \frac{\text{Sum of all observations}}{\text{No. of observations}}$

$25 = \frac{\text{Sum of ages of 4 members}}{4}$

$25 \times 4 = \text{Sum of all observations}$

$100 = \text{Sum of all observations}$

We are given that  if the age of head of family is also included in the average age is increased by 20%

So, New mean = 25+20\%(25)=30

So, Number of people = 4+1=5

$30 = \frac{\text{Sum of ages of 5 members}}{5}$

$150 = \text{Sum of ages of 5 members}$

Age of Head family = 150-100 = 50

Hence The age of head of the family is 50

#Learn more:

The Average age of 7 members of a family is 18 years . if the head of the family is excluded , then the average age of the rest of the members would be 5 years less. find the age of the head of the family.

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