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:
Answer & explanation
Correct answer: option 3
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