The average age of the boys in the class was 16 years. When 4 boys whose average age was 13 years are admitted to the class, the average age of the class was reduced by 6 months. How many boys were there initially in the class?

Correct option is B

Let the number of boys initially be x

Initially the sum of age of all students in the class = 16x

Total age of all the four boys who admitted new in the school = 4$$\times 13= 52$$ 

Final Sum of age of all the students in the class = 20 (x+ 15.5)

ATQ

16x+ 52 = 15.5 (x+ 4)

x = 20