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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 

`(4"a" + 9"b")/(4"c" + 9"d") = (4"a" - 9"b")/(4"c" - 9"d")`

Solution

`(4"a" + 9"b")/(4"c" + 9"d") = (4"a" - 9"b")/(4"c" - 9"d")`

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

Multiplying both sides by  `4/9`

`=> "a"/"b" xx 4/9 = "c"/"d" xx 4/9`

`=> (4"a")/(9"b") = (4"c")/(9"d")`

Applying componendo and dividendo, 

`(4"a" + 9"b")/(4"a" - 9"b") = (4"c" + 9"d")/(4"c" - 9"d")`

`=> (4"a" + 9"b")/(4"c" + 9"d") = (4"a" - 9"b")/(4"c" - 9"d")`

Hence, 4a + 9b : 4c + 9d = 4a - 9b : 4c - 9d 

  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 9.3 | Q: 1.3

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