Question

The sum of the digit of a two-digit number is 11. The number is less than the number obtained by interchanging the digit by 9. Find the number​

Answer 1

Let the digit at units place be x

Then, the digit at the tens place = 11 - x

The number = 10 ( 11 - x ) + x

Number formed by interchanging digits = 10x + 11 - x

10 ( 11 - x ) + x + 9 = 10x + 11 - x

110 - 10x + x + 9 = 9x + 11

-9x + 119 = 9x + 11

-18x = -108

x = 6

Therefore the number = 10 ( 11 - 6 ) + 6

= 10 × 5 + 6

= 56

Hope this helps :)