The average age of 8 men is increased by 2 ye | vedclass

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(B) Let the initial average age of $8$ men be $x$ years.Sum of the ages of $8$ men $= 8x$ years.When $2$ men are replaced by $2$ women,the new average

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(B) Let the initial average age of $8$ men be $x$ years.Sum of the ages of $8$ men $= 8x$ years.When $2$ men are replaced by $2$ women,the new average age becomes $(x + 2)$ years.Sum of the ages of the new group $= 8(x + 2) = 8x + 16$ years.The increase in the total sum of ages is $(8x + 16) - 8x = 16$ years.This increase is due to the difference between the ages of the $2$ women and the $2$ men replaced.Sum of the ages of $2$ women $=$ (Sum of the ages of $2$ replaced men) $+ 16$.Sum of the ages of $2$ women $= (20 + 24) + 16 = 44 + 16 = 60$ years.Average age of the $2$ women $= \frac{60}{2} = 30$ years.

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)?

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