The average age of a group of persons going f | vedclass

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(B) Let the number of persons initially going for the picnic be $x$.The total age of the initial group is $16.75x$.The total age of the $20$ new perso

Vedclass · Accepted Answer

$20$

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(B) Let the number of persons initially going for the picnic be $x$.The total age of the initial group is $16.75x$.The total age of the $20$ new persons is $20 	imes 13.25 = 265$.The total number of persons after joining is $(x + 20)$.The new average age is $15 	ext{ years}$,so the total age is $15(x + 20)$.Equating the total ages: $16.75x + 265 = 15(x + 20)$.$16.75x + 265 = 15x + 300$.$16.75x - 15x = 300 - 265$.$1.75x = 35$.$x = \frac{35}{1.75} = \frac{3500}{175} = 20$.Therefore,the number of persons initially going for the picnic is $20$.

The average age of a group of persons going for a picnic is $16.75 \text{ years}$. $20$ new persons with an average age of $13.25 \text{ years}$ join the group on the spot,due to which the average age of the group becomes $15 \text{ years}$. Find the number of persons initially going for the picnic.

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