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Question 1087803: the difference of digits of two digits numbers is 3.if we interchange the numbers we get diminished by original number by 27.findd the number?
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! The solution is not unique.
Let the number be 10t + u, where t = tens digit & u = units digit
| t - u | = 3 so if t > u then t-u=3, and if u > t then u-t = 3
Also, we are given that the number is diminished by 27 if the digits are reversed.
That means
10u+t = (10t+u)-27
9u - 9t = -27
u - t = -3 —> t - u = +3 —> t > u (tens digit > unit digit)
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Choose u=6. Then t=9. —> that gives us 96 — Check: 96 - 27 = 69 (digits swapped if we subtract 27, so ok)
Other answers are 85, 74, 63, 52, 41 and if we take the liberty of calling "03" a two digit number then 30 is also included.
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Spot check:
41 - 27 = 14
52 - 27 = 25
etc.
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