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

The average of the three numbers x, y, and z is 45. x greater than the average of y and z by 9. The average of y and z is grater than y by 2. Then the difference of x and z is: Correct Answer 7

Solution(By Examveda Team)According to the question, ⇒x+y+z/3=45⇒x+y+z=135.....(i)⇒x-9=y+z/2⇒2x−y−z=18.....(ii) now(i)+(ii)x+y+z=1352x-y-z=18________________3x=153x=51From (i)y + z = 135 - 51 = 84.....(iii)Also, ⇒y+z/2=y+2⇒y+z=2y+4⇒-y+z=4…….(iv)now, (iii)+(iv)  y+z=84-y+z=4_________2z=88⇒ z=44Required difference= 51 - 44 = 7

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