Question

Q. The average weight of the students of a class is 60 kg. If eight new students of

average weight 64 kg join the class, the average weight of the entire class becomes 62
kg. How many students were there in the class initially ?

Answer 1

8

Explanation:

Let's assume that initially there were 'n' students in the class, with an average weight of 60 kg.

So, the total weight of all the students in the class initially would be n * 60.

After eight new students of average weight 64 kg join the class, the total weight of all students in the class becomes (n+8) * 62.

We can set up an equation based on the above information:

(n * 60 + 8 * 64) / (n + 8) = 62

Simplifying this equation, we get:

60n + 512 = 62n + 496

2n = 16

n = 8

Therefore, initially there were 8 students in the class.

Answer 2

Answer and Step-by-step explanation:

Let's solve this problem step by step:

Let's assume that the initial number of students in the class is "x".

Given:

Average weight of the students in the class = 60 kg

Average weight of the new students = 64 kg

Average weight of the entire class after the new students join = 62 kg

Step 1: Calculate the total weight of the students in the class initially.

Total weight of the students in the class initially = Average weight * Number of students

Total weight of the students in the class initially = 60 kg * x

Step 2: Calculate the total weight of the new students.

Total weight of the new students = Average weight of the new students * Number of new students

Total weight of the new students = 64 kg * 8

Step 3: Calculate the total weight of the entire class after the new students join.

Total weight of the entire class after the new students join = Average weight of the entire class after the new students join * Total number of students in the class after the new students join

Total weight of the entire class after the new students join = 62 kg * (x + 8)

Step 4: Set up the equation.

According to the given information, the total weight of the students in the class initially plus the total weight of the new students should be equal to the total weight of the entire class after the new students join.

60 kg * x + 64 kg * 8 = 62 kg * (x + 8)

Step 5: Solve the equation to find the value of "x".

60x + 512 = 62x + 496

2x = 16

x = 8

Therefore, the initial number of students in the class was 8.