Question

Q3. The average weight of some students in a class is 62 kg. lf 8 students of average weight 55 kg leave
the class and 13 students of average weight 65 kg join the class,
then the average weight of the remaining
students in the class is 63.9 kg. The number of students in the class, initially was
​

Answer 1

Answer:

Let there be n students in the class.

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

62n−60n=64(8)−62(8)

2n=16

n=8

Therefore, initially there were 8 students in the class.

Answer 2

Given,

The average weight of some students = 62kg

8 students with an average weight of 55kg leave the class

13 students with an average weight of 65kg join the class

the average weight of the remaining students = 63.9kg

To find,

The number of students in the class initially.

Solution,

We can solve this question easily using linear equations and the concept of average.

Let the number of students initially present in the class be = x

then the weight of all the students = 62x (∵ total = avg × no. of things)

when 8 students leave the class, the weight of the remaining

students = 62n - 8(55)

and when other 13 students join the class, the weight of all students =

62n - 8(55) + 13(65) = 63.9 (n - 8 + 13)

⇒ 62n = 63.9(n+5) + 440 - 845

⇒62n - 63.9n = 319.5 - 405

⇒ - 1.9n = -85.5

⇒ x = 45

∴ The total number of students in the class initially were 45.