Question

The average age of
a group of friends is
18 years. Two people
aged 21 and 25
years join the group
making the average
age go up by an
even number. How
many members were
originally there in the
group?​

Answer 1

Answer:

4.(I think this one only)

Answer 2

SOLUTION

GIVEN

• The average age of a group of friends is 18 years.

• Two people aged 21 and 25 years join the group making the average age go up by an even number.

TO DETERMINE

The number members were originally there in the group

EVALUATION

Let the number members were originally there in the group = x

The average age of a group of friends is 18 years.

So the sum of their ages = 18x years

Now two people aged 21 and 25 years join the group making the average age go up by an even number.

Suppose 2n be the even number by which the age of the gro is increased

Since two people aged 21 and 25 years join the group

So the sum of their new age

= 18x + 21 + 25

= 18x + 46

Average age

$\displaystyle \sf{ = \frac{18x + 46}{x + 2} }$

So by the given condition

$\displaystyle \sf{ \frac{18x + 46}{x + 2} - 18 = 2n }$

$\displaystyle \sf{ \implies \frac{18x + 46 - 18x - 36}{x + 2} = 2n }$

$\displaystyle \sf{ \implies \frac{10}{x + 2} = 2n }$

$\displaystyle \sf{ \implies \frac{5}{x + 2} = n }$

Since x and n both are natural number

So the above equality holds only if x = 3

Then n becomes 1

Which is valid

Hence the number members were originally there in the group = 3

FINAL ANSWER

The number members were originally there in the group = 3

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