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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:

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: Correct Answer 7

According to the question, ⇒(x + y + z)/3 = 45 ⇒x + y + z = 135.....(i) ⇒x = (y + z)/2 + 9 ⇒2x−y−z = 18.....(ii) x + y + z = 135 2x−y−z = 18 −−−−−−−−−−−− 3x = 153 x = 51 From (i) y + z = 135 - 51 = 84.....(iii) Also, ⇒(y + z)/2 = y + 2 ⇒y + z = 2y + 4 ⇒z−y = 4 + y + z = 84 −y + z = 4 −−−−−−−−− 2z = 88 z = 44 Required difference = 51 - 44 = 7

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