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:

7

ATQ

x - \(\frac{y + z}{2}\) = 9

2x - y - z = 18 -------- (i)

\(\frac{y + z}{2}\) - y = 2

y + z - 2y = 4

z - y = 4 ---------- (ii)

Put the value of y = z - 4 from eqn (ii) to eqn (i)

2x - z + 4 - z = 18

2(x - z) = 14

⇒ x - z = 7