Question

The sum of the digits of a two digit no is 9.if 9 is added to the number,the digits interchange their places find the number.

Answer 1

Let us assume x and y are the digits of the number.

Therefore, the two-digit number is 10x + y

Given:

x + y = 9  ---------------1

Also given:

10x + y + 9 = 10y + x

9y – 9x = 9

y – x = 1

y = x + 1 ---------------2

Substitute the value of y from eqn 2 in eqn 1

x + x + 1 = 9

2x = 8

x = 4

Therefore, y = x + 1 = 4 + 1 = 5

The two-digit number = 10x + y = (10*4) + 5 = 45