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The average age of 30 students of a class is 14…

September 7, 2022 by Prabhat

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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

Answer: Option A

Here is complete explanation of The average age of 30 students of a class is 14….

Solution(By ExamCraze Team)

According to the question,
Total age of 30 students
= 30 × (14 years 4 months)
= 30 × $$14frac{1}{3}$$
= $$frac{30 × 43}{3}$$
= 430 years
Total age of (30 + 5) students = 35 (13 years 9 months)
= 35 × $$13frac{3}{4}$$
= $$frac{1925}{4}$$ 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