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If `(5x + 6y)/(5u + 6v) = (5x - 6y)/(5u - 6v)` Then Prove that X : Y = U : V - Mathematics

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Question

If `(5x + 6y)/(5u + 6v) = (5x - 6y)/(5u - 6v)` then prove that x : y = u : v

Solution

`(5x + 6y)/(5u + 6v) = (5x - 6y)/(5u - 6v)`   (By aletrnendo)

`(5x + 6y)/(5x - 6y) = (5u + 6v)/(5u - 6v)`

`(5x + 6y + 5x - 6y)/(5x + 6y - 5x + 6y) = (5u + 6v + 5u - 6v)/(5u + 6v - 5u = 6v)`    (By componendo and dividendo)

`(10x)/(12y) = (10u)/(12v)`

`x/y = u/v`

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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(C) | Q: 4 | Page no. 101
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If `(5x + 6y)/(5u + 6v) = (5x - 6y)/(5u - 6v)` Then Prove that X : Y = U : V Concept: Componendo and Dividendo Properties.
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