Average age of 7 students of a class is 28 years. Average age of first three students is 30 years. Age of fourth student is 4 years less than the age of fifth student. Ages of last two students is same and is 5 more than the average age of first three students. What is the average age of fourth and fifth student?

A. 20 years

B. 36 years

C. 18 years

D. 16 years

Answer: Option C

Solution(By Examveda Team)

Total age of 7 students = 7 x 28 = 196 years
Total age of first 3 students = 3 x 30 = 90 years
5^th student age = x years
4^th student age = (x + 4) years
Age of 6^th and 7^th student = 30 + 5 = 35 years
Total age of 7 students = 196
⇒ 90 + (x + 4) + (x) + 35 + 35 = 196
⇒ 2x = 196 - 164
⇒ 2x = 32
∴ x = 16 years
Average of 4^th and 5^th student
$$\eqalign{ & = \frac{{\left( {x + 4} \right) + x}}{2} \cr & = \frac{{2 \times 16 + 4}}{2} \cr & = 18{\text{ years}} \cr} $$