Question

The sum of the digits of a two-digit number is 10. If the digits are reversed, a new number is formed. The new number is one less than twice the original number. How do you find the original number?

Answer 1

Original number was `37`

Explanation:

Let `m and n` be the first and second digits respectively of the original number.

We are told that: `m+n=10`
`-> n=10-m` [A]

Now. to form the new number we must reverse the digits. Since we can assume both numbers to be decimal, the value of the original number is `10xxm+n` [B]

and the new number is: `10xxn+m` [C]

We are also told that the new number is twice the original number minus 1.

Combining [B] and [C] `-> 10n+m = 2(10m+n)-1` [D]

Replacing [A] in [D]

`-> 10(10-m)+m = 20m +2(10-m)-1`

`100-10m+m=20m+20-2m-1`

`100-9m = 18m+19`

`27m = 81`

`m=3`

Since `m+n =10 -> n=7`

Hence the original number was: `37`

Check: New number `=73`

`73 = 2xx37-1`