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Mathematics

If p, q, and r are in continued proportion, then :

  1. p : q = p : r

  2. q : r = p2 : q2

  3. p : q2 = r : p2

  4. p : r = p2 : q2

Ratio Proportion

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Answer

Since, p, q, and r are in continued proportion.

∴pq=qr⇒q2=pr ……..(1)\therefore \dfrac{p}{q} = \dfrac{q}{r} \\[1em] \Rightarrow q^2 = pr \text{ ……..(1)}

Solving,

p : r = p2 : q2

⇒pr=p2q2⇒q2=p2×rp⇒q2=pr ………(2)\Rightarrow \dfrac{p}{r} = \dfrac{p^2}{q^2} \\[1em] \Rightarrow q^2 = \dfrac{p^2 \times r}{p} \\[1em] \Rightarrow q^2 = pr \text{ ………(2)}

Since, equation (1) and (2) are equal.

Hence, Option 4 is the correct option.

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