Question

the average weight of a class is 42.5kg.if 5 new student whose weight respectively are 44.5,53.5,42.5,41.5and 43kg join the average weight becomes 42.6. Find the no. of students in start.

Answer 1

Given:

The average weight of a class is 42.5 kg

5 new students whose weight respectively are 44.5, 53.5, 42.5, 41.5 and 43 kg joins

New average weight = 42.6 kg

To find:

The no. of students in start

Solution:

Let "x" represent the initial no. of students.

So,

The sum of weights of the students initially present in the class = (42.5 x) kg

No. of students after 5 new students had joined = x + 5

Total weight of 5 new students = 44.5 + 53.5 + 42.5 + 41.5 + 43 = 225 kg

We know the formula of the average is given as,

$Average = \frac{Sum \:of\: observations}{No.\: of\: observations}$

Now, based on the formula of average we can form an equation as,

$42.6 = \frac{42.5x\:+\:225}{x\:+\:5}$

⇒ $42.6 [x\:+\:5] = 42.5x\:+\:225$

⇒ $42.6x + 213 = 42.5x + 225$

⇒ $42.6x - 42.5x = 225 - 213$

⇒ $0.1x = 12$

⇒ $x = \frac{12}{0.1}$

⇒ $\bold{x = 120}$

Thus, the no. of students in start was 120.

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