Question

The average weight of the students of a class is $60kg$. If eight new students of average weight $64kg$ join the class, the average weight of the entire class becomes $62kg$. How many students were there in the class initially?

Answer 1

Hint: In this question, we are given the average weight of class of students and the new average when eight more students join the class. The average weight of the eight students who have just joined is also given. We are asked the number of students who were there in the class initially. Start by finding the sum of weights of the children initially in the class and then the sum of weights of eight people who just joined. Divide the total sum by the number of students and equate it with the new average. By simplifying, you will find the number of students initially.

Complete step-by-step solution:
We are given the average weight of class of students and the new average when eight more students join the class. The average weight of the eight students who have just joined is also given. We are asked the number of students who were there in the class initially.
We will start by making an equation from each sentence of the question. Let the number of students in the class initially be $x$.
We know that, Mean = $\dfrac{{{\text{Sum of observations}}}}{{{\text{Total observations}}}}$
The average weight of the students of a class is $60kg$.
$ \Rightarrow 60 = \dfrac{{{\text{Sum}}}}{x}$
$ \Rightarrow {\text{sum = 60}}x$
The sum of the weight of $x$number of students is $60x$.
The average weight of eight students is $64kg$.
$ \Rightarrow 64 = \dfrac{{{\text{Sum}}}}{8}$
$ \Rightarrow {\text{sum = }}64 \times 8 = 512$
The sum of the weight of eight students is $512kg$.
The average weight of the entire classroom is $62kg$.
Total number of students = $x + 8$
Sum of their ages = $(60x + 512)kg$
Putting in the formula, Mean = $\dfrac{{{\text{Sum of observations}}}}{{{\text{Total observations}}}}$
$ \Rightarrow $$62 = \dfrac{{60x + 512}}{{x + 8}}$
Solving for x,
$ \Rightarrow 62(x + 8) = 60x + 512$
$ \Rightarrow 62x + 496 = 60x + 512$
Shifting and solving,
$ \Rightarrow 62x - 60x = 512 - 496$
$ \Rightarrow 2x = 16$
$ \Rightarrow x = \dfrac{{16}}{2} = 8$

Hence, there were 8 students initially.

Note: Mean is a statistical indicator that can be used to gauge the performance of a company’s stock price over a period of days, months, or years, a company through its earnings over a number of years, a film by assessing its fundamentals such as price-to-earnings ratio, free cash flow, and liabilities on the balance sheet, and a portfolio by estimating its average returns over a certain period.