Question

The average age of 30 boys in a class is 15 years. One boy aged 20 years left the class, but two new boys come in his place whose ages differ by 5 years. If the average age of all the boys now in the class still remains 15 years, the age of the younger new comer is 

(a) 20 years 

(b) 15 years 

(c) 10 years 

(d) 8 years

Answer 1

Answer is: (b) 15 years.

Total age of 30 boys = 30 × 15 = 450 

Total age of the rest of boys after the boy aged 20 years leaves = 450 – 20 = 430 

Let x be the age of the younger new comer.

Then, \(\frac{430+x+(x+5)}{31}\) = 15

⇒ 435 + 2x = 31 × 15 = 465 

⇒ 2x = 30 ⇒ x = 15 years.