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If ( A+C): B = 5: 1 and (Bc+Cd): Bd = 5: 1, Then Prove that A: B = C: D - ICSE Class 10 - Mathematics

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Question

If ( a+c) : b = 5 : 1 and (bc + cd) : bd = 5 : 1, then prove that a : b = c : d 

Solution

`("a + c")/"b" = 5/1`

⇒ a + c = 5b

`("bc + cd")/"bd" = 5/1`

⇒  bc + cd = 5bd 

⇒ bc +cd = (a + c)d

⇒ bc + cd = ad + cd

⇒ bc = ad

⇒ `"a"/"b" = "c"/"d"`

Hence a : b = c : d

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APPEARS IN

 Frank Solution for Frank Class 10 Mathematics Part 2 (2016 to Current)
Chapter 9: Ratio and Proportion
Exercise 9.2 | Q: 12

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Solution If ( A+C): B = 5: 1 and (Bc+Cd): Bd = 5: 1, Then Prove that A: B = C: D Concept: Proportions.
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