### The average of the three numbers x, y and z is 45. x is greater than the average of y and z by 9. The average of y and z is greater than y by 2. Then the difference of x and z is :

A. 3 B. 5 C. 7 D. 8 Answer: Option C

### Solution(By Apex Team)

\begin{aligned}&\text{ According to the question, }\\ &\Rightarrow\frac{x+y+z}{3}=45\\ &\Rightarrow x+y+z=135\ldots\ldots(i)\\ &\Rightarrow x=\frac{y+z}{2}+9\\ &\Rightarrow2x-y-z=18\ldots\ldots(ii)\\ &x+y+z=135\\ &\frac{2x-y-z=18}{3x=153}\\ &x=51\end{aligned} \begin{aligned}&\text{ From (i) }\\ &y+z=135-51=84\ldots.\text{ (iii) }\\ &\text{ Also, }\\ &\Rightarrow\frac{y+z}{2}=y+2\\ &\Rightarrow y+z=2y+4\\ &\Rightarrow z-y=4\\ &+y+z=84\\ &\frac{-y+z=4}{2z=88}\\ &\Rightarrow z=44\\ &\text{Required difference}\\ &\text{= 51 – 44 = 7}\end{aligned}

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