Average age of 8 men is increased by 2, years. When 2 of them, whose ages are 20, years and 24 ,year

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The average age of $8$ men is increased by $2\, years.$ When $2$ of them, whose ages are $20\, years$ and $24 \,years$ respectively, are replaced by $2$ women. What is the average age of these two women ? (in $years$)

$36$

$30$

$40$

$42$

Solution

Let, the average age of $8$ men be $x$ years.

$\therefore$ Sum of the ages of $8$ men $=84$ years.

Now, according to the condition of the question, average age of $(6\, men +2 \,women )=(x+2)$ years.

$\therefore$ Sum of the ages of $(6 \,men +2$ women $)$ $=8(x+2)=8 x+16$ years

Hence, it is clear that on replacing $2 $men by $2$ women, sum of their ages increased by $16$ years. Therefore, sum of the ages of two women $=(20+24)+16=60$ years

$\therefore$ Average age of the women $=\frac{60}{2}=30$ years.

Standard 13

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hard

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Solution

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