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If a : B = C : D, Prove That: Xa + Yb : Xc + Yd = B : D. - Mathematics

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Question

If a : b = c : d, prove that: xa + yb : xc + yd = b : d.

Solution

Given `a/b = c/d`

`=> (xa)/(yb) = (xc)/(yd)`  (Multiplying each side by x/y)

`=> (xa = yb)/(yb) = (xc + yd)/(yd)` (By componendo)

`=> (xa + yb)/(xc + yd) = (yb)/(yd)`

`=> (xa + yb)/(xc + yd) = b/d`

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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: 1.3 | Page no. 101

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Solution If a : B = C : D, Prove That: Xa + Yb : Xc + Yd = B : D. Concept: Componendo and Dividendo Properties.
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