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Explanation:

Let the common ratio be ‘k’.
⇒ x = y/k and z = yk

Now considering the AP, 5x = 5y/k, 16y and 12z = 12yk are in arithmetic progression,
∴ 2 × 16y = 5y/k + 12yk
⇒ 32 = 5/k + 12k
⇒ 12k2 – 32k + 5 = 0
⇒ (2k – 5)(6k – 1) = 0
⇒ k = 5/2 or 1/6

As x < y < z, k has to be greater than 1.
∴ k = 5/2

Hence, option (b).

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