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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 

7a+11b : 7a -11b = 7c +11d : 7c - 11d 

Solution

7a+11b: 7a -11b = 7c+11d : 7c -11d 

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

Multiplying both sides by  `7/11`

`=> "a"/"b" xx 7/11 = "c"/"d" xx 7/11`

`=> (7"a")/(11"b") = (7"c")/(11"d")`

Applying componendo and dividendo, 

`(7"a" + 11"b")/(7"a" - 11"b") = (7"c" + 11"d")/(7"c" - 11"d")`

Hence, 7a+11b : 7a -11b = 7c +11d : 7c - 11d 

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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: 1.2

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