Question

A two-digit number whose sum of digits is 14. If 36 is added to the number, the digts are interchanged. How do you find the number?

Answer 1

Number is `59`

Explanation:

Let the unit's digit be `x` as sum of digits is `14`, ten's digit is `14-x`,

then the number is `10xx(14-x)+x`

i.e. `140-10x+x` or `140-9x`

Reversing the digits number, unit digit becomes `14-x` and tens digit becomes `x`, hence number is `10x+14-x=9x+14`.

As adding `36` to `140-9x` makes it `9x+14`, we have

`140-9x+36=9x+14`

or `176-14=9x+9x`

or `18x=162`

or `x=9`

and hence, unit''s digit is `9` and tens digit is `5`

and number is `59`