Question

In a group of students, if a student aged 19 years is replaced by a student aged 25 years, the average age of the group increases by 0.4 years. Find the number of students in the group

Answer 1

The number of students in the group of students, if the average increases by 04 years on replacing a 19 year old student by a 25 year old student, is 15.

Step-by-step explanation:

Let the no. of students in the group of students be denoted as “x” and also the sum of the ages of these “x” no. of students including the 19-year-old student be “y” years.

We know that the formula of average is given by,

Average = (sum of quantities) / (number of quantities)

Therefore, we get

The average age of the group of students = $\frac{y}{x}$

It is given that if a 19-year-old student is replaced by a 25-year-old student, the average age of the group increases by 0.4 years.

So, we have

The sum of ages = [y - 19 + 25] years

And,

Mean = [$\frac{y}{x}$ + 0.4] years

Therefore, we can now write eq. as

⇒  [$\frac{y}{x}$ + 0.4] = [$\frac{y - 19 + 25}{x}$]

⇒  $\frac{y + 0.4 x}{x} = \frac{y + 6}{x}$

⇒  y + 0.4x = y + 6

⇒  0.4 x = 6

⇒  x = $\frac{6}{0.4}$

⇒  x = $\frac{60}{4}$

⇒  x = 15

Thus, the number of students in the group is 15.

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