Sum of the digits of a two digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two digit number?
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Answer:
Let the unit's digit be x.
Ten's digit = 9-x
New number = 10x+9-x=9x+9
Number after interchanged=10(9-x) + x = 90-10x+x = 90-9x
ACQ,
9x+9=90-9x+27
18x=108
x=6
Unit's digit = 6
Ten's digit = 3
Number = 36
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Answer Expert Verified
The new number is greater than the old number by 27, i.e. Adding the two equations, we get 2y = 12 or y = 6. Thus, x = 3. Therefore, the original number is 36.
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