The average age of 30 students of a class is 14 years 4 months. After admission of 5 new students in the class the average becomes 13 years 9 months. The youngest one of the five new students is 9 years 11 months old. The average age of the remaining 4 new students is :

Answer: Option A

According to the question,
Total age of 30 students
= 30 × (14 years 4 months)
= 30 × $$14\frac{1}{3}$$
= $$\frac{30\times 43}{3}$$
= 430 years
Total age of (30 + 5) students = 35 (13 years 9 months)
= 35 × $$13\frac{3}{4}$$
= $$\frac{1925}{4}$$ years
Total age of 5 students
= $$\frac{1925}{4}$$ - 430
= $$\frac{205}{4}$$
= 51 years 3 months
∴ One of the new five student is = 9 years 11 months old
⇒ Remaining 4 students age
= $$\frac{\text{41 years 4 months}}{4}$$
= 10 years 4 months