The average of 8 numbers is 20. The average of first two numbers is $$15\frac{1}{2}$$ and that of the next three is $$21\frac{1}{3}$$ . If the sixth number be less than the seventh and eighth numbers by 4 and 7 respectively, them the eighth number is :

A. 18

B. 22

C. 25

D. 27

Answer: Option C

Solution(By Examveda Team)

Let the sixth number = x
Then the seventh = x + 4
And the eighth = x + 7
According to the question,
$$ \Rightarrow 2 \times \frac{{31}}{2} + 3 \times \frac{{64}}{3} + x + x + 4 + x + 7$$        = 8 × 20
$$\eqalign{ & \Rightarrow 31 + 64 + 3x + 11 = 160 \cr & \Rightarrow 106 + 3x = 160 \cr & \Rightarrow 3x = 54 \cr & \Rightarrow x = 18 \cr} $$
∴ Eighth number x + 7 = 18 + 7 = 25