In a class, there are 25 students whose average age decreases by 3 months when one student aged 22 years is replaced by a new student. The age of the new student is:?

Option 3 : 15 Yrs 9 months

Formula

Average = sum of observation/number of observations

Calculation

Let the total age of 25  students be y months and average be x months

⇒ x = y/25     ------(i)

Now 1 student aged 22years or 22 × 12 months is replaced by student of λ years

The average of the 25 students decreases by 3 months then,

⇒ x - 3 = (y - 22 × 12 + λ )/25

⇒ x = 3 + (y - 22 × 12 + λ)/25      ------(ii)

From eq (i) and (ii) we get,

⇒ y/25 = 3 +(y - 22 × 12 + λ)/25

⇒ y = 75 + y - 264 + λ 

⇒ λ = 189 months

∴ The age of new student is 15 years 9 months