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A family consists of 5 elders and some children, such that the average age of the family is 28 years. If the average age of the elders and the children is 42 years and 18 years respectively, how many children are there in the family?

A family consists of 5 elders and some children, such that the average age of the family is 28 years. If the average age of the elders and the children is 42 years and 18 years respectively, how many children are there in the family? Correct Answer 7

Given:

Average of a family = 28 years

The average of 5 elders = 42 years

The average of children = 18 years

Formula used:

Average = Sum of observation/Total number of observation

Calculation:

Let there be ‘x’ children in the family.

⇒ Total age of x children = 18x years

⇒ Total age of 5 elders = 5 × 42 = 210 years

Now,

Total no. of family members = 5 + x

⇒ Total age of family = 28(5 + x) = 140 + 28x

⇒ 140 + 28x = 18x + 210

⇒ 10x = 70

⇒ x = 70/10 = 7

∴ There are 7 children in the family

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Elders : Childern = 10x : 14x = 5x : 7x

Elders = 5x = 5

x = 1

Childerns 7 × 1 = 7

∴ There are 7 children in the family

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