#### 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 be the three quantities which are in continued proportion.

Then, x : y :: y : z ⇒ y^{2} = xz ….(1)

Now, we have to prove that

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

That is we need to prove that

xy^{2 }= x^{2}z

LHS = xy^{2} = x(xz) = x^{2}z = RHS [Using (1)]

Hence, proved.

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.