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
$\begin{array}{l}\text{⇒ Remaining 4 students age}\\
\begin{array}{l}
=\Large\frac{41 \text { years } 4 \text { months }}{4} \\
=10 \text { years } 4 \text { months }
\end{array}\end{array}$
