Question

The average age of a group of friends is 34 years. If five new friends with an average of 30 years age join the group, the average age of the entire group becomes 32 years. The number of friends in the group initially is

Answer 1

Answer:

The number of friends in the group initially is 5

Step-by-step explanation:

Let "n" be the number of friends originally in the group.

As their average age is 34, the sum of their ages = 34*n

Now, five new friends enter the group. Their average age is 30. Hence, the sum of their ages = 150

Reason: average = sum of observations/number of observations

The sum of ages of all the friends = 34n + 150

The average age of all the friends = 32 .......(given)

The number of friends totally = n + 5

Hence:

(34n + 150)/(n+5) = 32 .......using definition of average

34n + 150 = 32*(n+2) ........cross multiplying

34n + 150 = 32n + 160

34n - 32n = 160 - 150

2n = 10

n = 5

The original number of friends is 5.

Verify:

Five original friends have average age 34, so sum of ages = 34*5 = 170

Five new friends enter with average age 30, so sum of their ages = 30*5 = 150

Sum of ages of all 10 friends = 170 + 150 = 320

Average age of all 10 friends = 320/10 = 32 (as given)