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?

1 Answer
Alan N.
May 21, 2018

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

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