The average of the three numbers x y and z is…

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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 :

  1. A. 3
  2. B. 5
  3. C. 7
  4. D. 8

Answer: Option C

Here is complete explanation of The average of the three numbers x y and z is….

Solution(By ExamCraze Team)

According to the question,
$$eqalign{ & Rightarrow frac{{x + y + z}}{3} = 45 cr & Rightarrow x + y + z = 135.....(i) cr & Rightarrow x = frac{{y + z}}{2} + 9 cr & Rightarrow 2x - y - z = 18.....(ii) cr & x + y + z = 135 cr & underline {2x - y - z = 18} cr & 3x = 153 cr & x = 51 cr} $$
From (i)
y + z = 135 - 51 = 84.....(iii)
Also,
$$eqalign{ & Rightarrow frac{{y + z}}{2} = y + 2 cr & Rightarrow y + z = 2y + 4 cr & Rightarrow z - y = 4 cr & + y + z = 84 cr & underline { - y + z = 4} cr & ,,,,,,,,,2z = 88 cr & ,,,,,,,,,,,,z = 44 cr} $$
Required difference
= 51 - 44 = 7

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