Question

The tens digit of a two-digit number exceeds the units digit by 5. If the digits are reversed, the new number is less by 45. If the sum of their digitsis 9, find the numbers.

Answer 1

Let the number be xy = 10x+y

when the number is reversed = yx = 10y+x

Given,

If the digits are reversed, the new number is less by 45

10x+y-(10y+x)=45

9x-9y=45

x-y=5...........(1)

Also given, the sum of their digitsis 9

x+y=5..................(2)

Adding (1)&(2), we get

2x=14

x=7

y=2

So, number is 72