Question

The average age of a group of 10 students was 14. The average age increased by 1 year when two new students joined the group. What is the average age of the two new students who joined the group?

Answer 1

16
because
(14+x)/2=15
x=(15)2-14
x=16

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Answer 2

The average age of the two new students who joined the group is 20 years.

Given,

The average age of a group of 10 students was 14,

It increased by 1 year after 2 new students joined.

To find,

The average age of the two new students who joined the group.

Solution,

The average can be defined as the total sum of the given quantities divided by the number of quantities.

Let the sum be S, and the number of quantities is N, then the average is given by,

$average(A)=\frac{S}{N}$     ...(1)

Here, initially, the average age of 10 (N₁) students (say A₁) is given to be 14.

So, from eq. (1),

$A_1=\frac{S_1}{N_1}$

$\implies 14=\frac{S_1}{10}$

Rearranging the above relation, we can find the sum of the ages of 10 students. That is,

S₁ = 14×10

⇒ S₁ = 140

Now, when 2 new students joined, the total number of students will be

N₂ = 10 + 2

⇒ N₂ = 12,

And the average age increased by 1. So, the new average is

A₂ = 14 + 1

⇒ A₂ = 15.

Let the sum of the ages of the two new students be S₂.

Now, it can be observed that the new average (A₂) can be determined as,

$A_2=\frac{S_1+S_2}{N_2}$

Substituting the respective values, we get,

$15=\frac{140+S_2}{12}$

Simplifying and rearranging,

$S_2=(15 \times 12) - 140$

$\implies S_2=180 - 140$

$\implies S_2=40$

Now, the average age of 2 new students who joined the group can be found using the above sum (S₂ = 40), as follows.

$average=\frac{S_2}{2} =\frac{40}{2}$

⇒ average = 20 years.

Therefore, the average age of the two new students who joined the group is 20 years.