Average age of a group of persons going for a picnic is 16.75 ,years. 20 new persons with an average

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

A

$24$

B

$20$

C

$15$

D

$18$

Solution

Let the person initially going for picnic is $x$

$16.75 \times x+20 \times 13.25=15(x+20)$

$1.75 x=15 \times 20-20 \times 13.25$

$1.75 x=35 \Rightarrow x=20$

Standard 13

Quantitative Aptitude

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