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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 :
- A. 3
- B. 5
- C. 7
- 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
