Question

the average age of 25boys in a class decreases by 6 months when a new boy takes the place of a 20 years old boy find the age of new boy​

Answer 1

Answer:

The average of new boy is 7.5 years.

New boy of age 'y' years is added and an old boy of age 20 years is removed. Also, in the question, it is told that the average age of 25 boys decreases by 6 months ( 0.5 years), when the substitution takes place. Thus, the avg. age of new boy is 7.5 years.

Answer 2

Step-by-step explanation:

The average of new boy is 7.5 years.

Let the average age of 25 boys initially be x years.

∴ Total age of 25 boys initially = (25×x) years = 25x years.

Let the age of the new boy be y years.

New boy of age 'y' years is added and an old boy of age 20 years is removed.

So, the total age of 25 boys now = (25x + y - 20) years

And the average age becomes = [(25x + y - 20) / 25] years ...(1)

Also, in the question, it is told that the average age of 25 boys decreases by 6 months ( 0.5 years), when the substitution takes place.

∴ Initial avg. age - Final avg. age = 0.5

⇒ x - [(25x + y - 20) / 25] = 0.5

⇒ 25x/25 - [(25x + y - 20) / 25] = 0.5

⇒ 20 - y = 25 × 0.5

⇒ y = 20 - 12.5 = 7.5

Thus, the avg. age of new boy is 7.5 years.