If   H.M. : G.M. = 4 : 5 for the two positive numbers, then the ratio of the numbers is

Let the numbers be a and b. Then, 2aba+bab=45⇒2aba+b=45⇒a+b2ab=54⇒a+b+2aba+b−2ab=5+45−4⇒a+ba−b2=91⇒a+ba−b=31⇒ab=3+13−1⇒ab=41Applying componendo and dividendo