#### Question

If three quantities are in continued proportion, show that the ratio of the first to the third is the duplicate ratio of the first to the second.

#### Solution

Let x, y and z are the three quantities which are in continued proportion

Then, x : y :: y : z => y^{2} = xz

Now, we have to prove that

x : z = x^{2} : y^{2}

⇒ xy^{2} = x^{2}z

LHS

= xy^{2} = x(xz) = x^{2}z = RHS

LHS = RHS

Is there an error in this question or solution?

Solution If Three Quantities Are in Continued Proportion, Show that the Ratio of the First to the Third is the Duplicate Ratio of the First to the Second. Concept: Proportions.