Question

The average age of 11 members of a cricket team reduces by 2 when two players of ages 30 and 32 leave the team and two new players of equal age join it. The age of each of the newcomers is _______.
A. 20 years
B. 62 years
C. 12 years
D. 22 years

Answer 1

Hint: To find the solution of this type of question we first assume the average age of 11 old team members and by using the above information we have to find the average age of 11 members including the new two members. Now since the subtraction of their average age is 2 so by using this we are able to find the ages of each newcomer.

Complete step-by-step answer:
Let us consider the age of each of the newcomers is x and let the average of the old team members age be A.
As we know that $$\text{average age} =\dfrac{\text{Summation of their age} }{\text{Total number of members} }$$
Therefore, $$A=\dfrac{\text{Summation of their age} }{11}$$
Now let the summation of the age of 9 members is S.
Therefore we can write,
$$A=\dfrac{S+30+32}{11}$$…………(1)
Again when two players of ages 30 and 32 leave the team and two new players of equal age x join then the average age(B) will be,
$$B=\dfrac{S+2x}{11}$$..................(2)
Now according to the question,
 A - B = 2
$$\Rightarrow \dfrac{S+30+32}{11} -\dfrac{S+2x}{11} =2$$
$$\Rightarrow \dfrac{S+62}{11} -\dfrac{S+2x}{11} =2$$
$$\Rightarrow \dfrac{(S+62)-(S+2x)}{11} =2$$
$$\Rightarrow \dfrac{S+62-S-2x}{11} =2$$
$$\Rightarrow \dfrac{62-2x}{11} =2$$
$$\Rightarrow 62-2x=2\times 11$$ [multiplying both side by 11]
$$\Rightarrow 62-2x=22$$
$$\Rightarrow -2x=22-62$$
$$\Rightarrow -2x=-40$$
$$\Rightarrow 2x=40$$ [multiplying both side by (-1)]
$$\Rightarrow x=\dfrac{40}{2}$$
$$\Rightarrow x=20$$
Therefore the age of each of the newcomers is 20 years.

So, the correct answer is “Option A”.

Note: So for this you need to know that to find the average or mean of the numbers you need to add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.
i.e, $$\text{Average number} =\dfrac{\text{Sum of all the numbers} }{\text{Count of numbers} }$$