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 :

A. 10 years 4 months

B. 12 years 4 months

C. 11 years 2 months

D. 13 years 6 months

Show Answer

Answer-A
Solution-

Solution(By Apex Team)

$\begin{array}{l}\text{According to the question,}\\ \text{Total age of 30 students}\\ \text{= 30 × (14 years 4 months)}\\ \begin{array}{l} =30 \times 14 \frac{1}{3} \\ =\Large\frac{30 \times 43}{3} \\ =430 \text { years } \end{array}\end{array}$ Total age of (30 + 5) students = 35 (13 years 9 months) $\begin{array}{l}=35\times13\frac{3}{4}\\ =\frac{1925}{4}\text{ years }\\ \text{Total age of 5 students}\\ \begin{array}{l}=\frac{1925}{4}-430\\ =\Large\frac{205}{4}\\ =51\text{ years }3\text{ months }\end{array}\end{array}$ ∴ One of the new five student is = 9 years 11 months old $\begin{array}{l}\text{⇒ Remaining 4 students age}\\ \begin{array}{l} =\Large\frac{41 \text { years } 4 \text { months }}{4} \\ =10 \text { years } 4 \text { months } \end{array}\end{array}$