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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. - ICSE Class 10 - Mathematics

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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 => y2 = xz 

Now, we have to prove that 

x : z = x2 : y2

⇒ xy2 = x2z

LHS

= xy2 = x(xz) = x2z = RHS

LHS = RHS

  Is there an error in this question or solution?

APPEARS IN

 Frank Solution for Frank Class 10 Mathematics Part 2 (2016 to Current)
Chapter 9: Ratio and Proportion
Exercise 9.2 | Q: 9

Video TutorialsVIEW ALL [1]

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.
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