Question

Average age of 25 boys in a class decreases by 6 months .When a new boy takes place of 20 years old boy.The average age of new boy is?

Answer 1

Answer:

Step-by-step explanation:

Total reduction in age=25*6/12=12.5years

Age of the new boy=20-12.5=7.5years

Answer 2

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.