###
**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**

## Show Answer

Solution(By Apex Team)

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

## Related Questions On Average

### Ajit has a certain average for 9 innings. In the tenth innings, he scores 100 runs thereby increasing his average19 people went to a hotel for combine dinner party 13 by 8 runs. His new average is:

A. 20B. 21

C. 28

D. 32

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### If the arithmetic mean of 0, 5, 4, 3 is a, that of -1, 0, 1, 5, 4, 3 is b and that of 5, 4, 3 is c, then the relation between a, b, and c is.

A. a = b = cB. a : b : c = 3 : 2 : 4

C. 4a = 5b = c

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