Question

Question #10969

Answer 1

`93`

Explanation:

I'm not sure if there an algebraic way to do this problem - I used guess and check.

First, find two digits that add up to `12`. Then reverse the number and subtract from the original number until you get a difference of `54`.

`7+5=12 -> 75-57 = 18`

`8+4=12 -> 84-48 = 36`

`9+3=12 -> 93-39 = 54`

So, the number is `93`.

Answer 2

Let x and y represents the digit of tens place and unit place respectively.

Then the number is `10x+y`

On reversing the digits we get the number `10y+x`

Hence by the 1st condition

`(10x+y)-(10y+x)=54`

`=>(9x-9y)=54`

`=>x-y=6........[1]`

Again by the 2nd condition

`x+y=12.......[2]`

Adding [1] and {[2] we get

`2x=18`

`=>x=9`

Inserting `x=9` in [2] we have

`y=3`

So the required number is `10x+y=10xx9+3=93`