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If a : B : : C : D, Then Prove that - ICSE Class 10 - Mathematics

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Question

If a : b : : c : d, then prove that 

(ax+ by): (cx + dy)=(ax - by) : (cx - dy) 

Solution

(ax+ by): (cx + dy)=(ax - by) : (cx - dy) 

`"a"/"b" = "c"/"d"`

Multiplying both sides by `"x"/"y"`

`=> "a"/"b" xx "x"/"y" = "c"/"d" xx "x"/"y"`

`=> ("ax")/("by") = ("cx")/("dy")`

Applying componendo and dividendo, 

`("ax+ by")/("ax - by") = ("cx + dy")/("cx - dy")`

` => ("ax+ by")/("cx + dy") = ("ax - by")/("cx - dy")`

Hence, ax + by : cx + dy = ax - by : cx - dy 

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APPEARS IN

 Frank Solution for Frank Class 10 Mathematics Part 2 (2016 to Current)
Chapter 9: Ratio and Proportion
Exercise 9.3 | Q: 1.4

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Solution If a : B : : C : D, Then Prove that Concept: Componendo and Dividendo Properties.
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