# The average age of a group of persons going on a trip is 16.75 years. 20 new persons with an average age of 13.25 years join the group on the spot due

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The average age of a group of persons going on a trip 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 yrs. find the number of persons initially going for the trip.
1. 21
2. 24
3. 20
4. 28

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Correct Answer - Option 3 : 20

Given:

Initial average = 16.75 years.

20 new persons with an average age of 13.25 years joined

New average = 15 yrs.

Formula:

Average of n numbers a1, a2, ………. an = (a1 + a2 + ... + an)/n

Calculation:

Let the no. of person initially going for the trip be x.

Total age of x persons = x × 16.75

Total age of 20 persons = 13.25 × 20 = 265

Total age of all the persons = 15 × (x + 20)

From the question

16.75x + 265 = 15(x + 20)

⇒ 16.75x + 265 = 15x + 300

⇒ 1.75x = 35

⇒ x = 20

∴ Initial number of person is 20