Question

Sum of the digits of a two digit number is 9. when we interchange the digits it is found that the resulting new number is greater than the original number by 63.find the two digit numbers

Answer 1

let the original number be xy and given that the sum of the digits is 9

⇒ x + y = 9

given that by interchanging digits the new number formed is greater than the original number by 63

⇒ xy + 63 = yx

⇒ 10x + y + 63 = 10y + x

⇒ 9x + 63 = 9y

⇒ 9(x - y) = -63

⇒ x - y = -7 and x + y = 9

⇒ 2x = 2

⇒ x = 1

⇒ y = 8

so the original number is 18 and the digits interchanged number is 81