Number System
The difference between a two-digit number and the number obtained by interchanging the two digits is 63. Which is the smaller of the two numbers?
Let the number be 10x + y∴ 3x = 4y ......(1)From (I),x + y = 14 .....(2)Solving equations (1) and (2),x = 8, y = 6∴ Number = 86 From (II)y = 75/100 x x ∴ 3x = 4y.Which is the same as eqn (1)
Let the two consecutive odd numbers be 2x - 1 and 2x + 1.(2x - 1) (2x - 1) = 4095= 4x² - 1 = 4095= 4x² = 4096= x² = 1024∴ x = 32∴ The numbers are 63 and 65.Greater number = 65