### The average of 8 numbers is 20. The average of first two numbers is $15 \large\frac{1}{2}$ and that of the next three is $21 \large\frac{1}{3}$ 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 Apex Team)

Let the sixth number = x Then the seventh = x + 4 And the eighth = x + 7 According to the question, $\begin{array}{l}\Rightarrow2\times\frac{31}{2}+3\times\frac{64}{3}+x+x\\ +4+x+7=8\times20\end{array}$ $\begin{array}{l}\Rightarrow31+64+3x+11=160\\ \Rightarrow106+3x=160\\ \Rightarrow3x=54\\ \Rightarrow x=18\end{array}$ ∴ Eighth number, x + 7 = 18 + 7 = 25

A. 20
B. 21
C. 28
D. 32

A. 18
B. 20
C. 24
D. 30

A. 10 years
B. 10.5 years
C. 11 years
D. 12 years