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.
Answers
Average age including head of the family = 18 yrs
Total age = 18*7 =126 yrs
Now, Without head of the family average age= 18-5 =13 years
Total age without head = 13* 6= 78 years
So, Age of head of the family = 126-78 = 48 years.
∴ The age of the head of the family is 48 years.
Given:
The average age of 7 members of a family is 18 years
The average age of all members of the family excluding the head is = 18-5 = 13 years
To Find:
The age of the head of the family
Solution:
Let us assume that:
1) the age of the head is 'x' years.
2) the sum of ages of all members except the head is = y years.
It is given that the number of members in the family = 7.
According to the question,
The average age of 7 members of a family is = 18 years
⇒ ( y + x)/7 = 18
⇒ y + x = 126 ...................................(I)
Also, the average age of all members of the family excluding the head is 5 years less than the average of the entire family.
⇒ y/6 = 18 - 5 = 13
⇒ y = 78 ...................................(II)
∴ The sum of the ages of the family members excluding the head = 78
Putting the value of equation (II) in (I) we get
78 + x = 126
⇒ The age of the head of the family, x = 126 - 78 = 48 years
∴ The age of the head of the family is 48 years.
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