Question

If a : b :: c : d, show that (2a + 3b) : (2c + 3d) :: (2a − 3b) : (2c − 3d).

Answer 1

a: b :: c : d

`a/b = c/d`

⇒ `(2a)/(3b) = (2c)/(3d)`   ...[Multiplying both side `2/3`]

Apply Componendo and Dividendo

`(2a + 3b)/(2a - 3b) = (2c + 3d)/(2c − 3d)`

⇒ `(2a + 3b)/(2c + 3d) = (2a − 3b)/(2c − 3d)`

Hence prove.