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.
- A$24$
- B$20$
- C$15$
- D$18$
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