Question

The average age of Seema, Sapna, Asha, Kavita and Atrye is 40 years. The average age of Seema and Sapna is 35 years and the average age of Asha and Kavita is 42 years. The age of Atrye is?
(A). 45
(B). 47
(C). 46
(D). 32

Answer 1

Hint: In this question it is given that the average age of Seema, Sapna, Asha, Kavita and Atrye is 40 years. The average age of Seema and Sapna is 35 years and the average age of Asha and Kavita is 42 years. Then we have to find the age of Atrye. So to find the solution we have to first consider the age of each person and after that by average formula we are going to find the solution.
So $$\text{average age} =\dfrac{\text{sum of the ages} }{\text{number of persons} }$$.

Complete step-by-step solution:
Let the age of Seema, Sapna, Asha, Kavita and Atrye be x, y, z, s and t respectively,
Then it is given, the average age of Seema, Sapna, Asha, Kavita and Atrye is 40 years,
Here number of person is 5, so we can write,
$$\dfrac{\text{sum of the ages} }{\text{number of persons} } =\text{average age} $$
$$\Rightarrow \dfrac{x+y+z+s+t}{4} =40$$
$$\Rightarrow x+y+z+s+t=40\times 5$$
$$\Rightarrow x+y+z+s+t=200$$.............(1)
Now also given that the average age of Seema and Sapna is 35.
$$\therefore \dfrac{x+y}{2} =35$$
$$\Rightarrow x+y=35\times 2$$
$$\Rightarrow x+y=70$$..................(2)
And the average age of Asha and Kavita is 42 years.
$$\therefore \dfrac{z+s}{2} =42$$
$$\Rightarrow z+s=42\times 2$$
$$\Rightarrow z+s=84$$..................(3)
Now putting the value of (x+y) and (z+s) in equation (1), we get,
$$x+y+z+s+t=200$$
$$\Rightarrow (x+y)+(z+s)+t=200$$
$$\Rightarrow 70+84+t=200$$
$$\Rightarrow 154+t=200$$
$$\Rightarrow t=200-154$$
$$\Rightarrow t=46$$
Therefore the age of Atrye is 46 years.
Hence the correct option is option C.

Note: In general if we write the average formula then we can write,
$$\text{Average value} =\dfrac{\text{Sum of observations} }{\text{Number of observations} }$$
But since in the above question the observation was age, so because of that we have written the average age formula.
Now the for a given data the average formula also can be expressed as,
$$\text{Average value} =\dfrac{x_{1}+x_{2}+x_{3}+\cdots +x_{n}}{n}$$
Where $$x_{1},x_{2},\ldots ,x_{n}$$ are the observations and n is the number of observations.