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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 - 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 be the three quantities which are in continued proportion.
Then, x : y :: y : z ⇒ y2 = xz ….(1)
Now, we have to prove that
x : z = x: y2
That is we need to prove that
xy= x2z
LHS = xy2 = x(xz) = x2z = RHS [Using (1)]
Hence, proved.

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#### APPEARS IN

Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Exercise 7(B) | Q: 11 | Page no. 94

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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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