Two numbers are in the ratio 9 : 16. If both numbers are increased by 40, then their ratio becomes 2 : 3, What is the difference between the two numbers?

56

                       I  :  II

Original ratio    9  :  16            

New ratio         2  :  3

____________________

                    +40    +40

⇒ $\frac{9R + 40}{16R+40} = \frac{2}{3}$

Using cross - multiplication method,

⇒ 32R - 27R = (40 x 3) - (40 x 2)

⇒            5R = 40

⇒             R = 8

Difference between I and II = 7R = 7 x 8 = 56