Given, `(a+3b+4c+5d)/(2a+3b-4c-5d)=(2a-3b+4c+5d)/(2a-3b-4c+5d)`
`implies((2a+3b)+(4c+5d))/((2a+3b)-(4c+5d))=((2a-3b)+(4c-5d))/((2a-3b)-(4c-5d))`
`implies(2a+3b)/(4c+5d)=(2a-3b)/(4c-5d)implies(2a+3b)/(2a-3b)=(4c+5d)/(4c-5d)`
Using componendo and dividendo rule,
`((2a+3b)+(2a-3b))/((2a+3b)-(2a-3b))=((4c+5d)+(4c-5d))/((4c+5d)-(4c-5d))`
`implies(4a)/(6b)=(8c)/(10d)implies(a)/(3b)=(2c)/(5d)`
`thereforea:3b: :2c:5d`
So, a,3b, 2c and 5d are in proportion
