#### 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

Is there an error in this question or solution?

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