Question

\the sum of the digits in a two digit number is 10. if the digits are reversed, the new number will be 54 more than the original number. what is the original number?

Answer 1

Answer: 28

Explanation:

Suppose the digits are a and b.

The original number is 10a+b

The reversed number is a+10b

We are given:

   a+b=10

   (a+10b)−(10a+b)=54

From the second of these equations we have:

   54=9b−9a=9(b−a)

Hence b−a=549=6, so b=a+6

Substituting this expression for b into the first equation we find:

a+a+6=10

Hence a=2, b=8 and the original number was 28

Hope this helps!