This question was previously asked in

HSSC Constable Female 30th December 2018 Official Paper

- 3
- 1/3
- 2
- 1/2

Option 2 : 1/3

**Calculation:**

⇒ 2y × 2 = x + 3z

⇒ 4y = x + 3z ---- (1)

Then,

⇒ y^{2} = xz

Common ratio r = y/x and r^{2 }= z/x

Dividing the equation (1) by x we'll get

4y/x = x/x + 3z/x

⇒ 4r = 1 + 3r^{2}

⇒ 3r^{2} - 4r + 1 = 0

⇒ 3r^{2} - 3r - r + 1 = 0

⇒ 3r(r - 1) - 1(r - 1) = 0

⇒ (3r - 1)(r - 1) = 0

r = 1/3 and r = 1

As, x, y and z are distinct so r ≠ 1.

**∴ Common ratio is 1/3.**

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