Question

The average age of 5 children of a family is 10 years but if we include the age of father and mother then the average age becomes 22 years. It is given that father age is 6 years more than the mother so what will be the age of mother at present.

Answer 1

The average age of $5$ children is $10years$

$\therefore$ Total age of $5$ children $=(5\times 10)years=50years$

Average of family when mother and father included its becomes $22years$

$\Rightarrow$Total age of $7$ members in family $=(7\times 22)years=154years$

$\Rightarrow$ Total mother and father age $=154-50=104years$

Let $x$ be the mothers age and $y$ be the fathers age.

$\therefore$ $x+y=104$ ------- ( 1 )

According to the question,

$y=x+6$

$\therefore$ $-x+y=6$ ------ ( 2 )

Subtracting ( 2 ) from ( 1 ) we get,

$2x=98$

$\therefore$ $x=49$

$\therefore$ The present age of mother is $49years$