Q.3 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?
Given that sum of the two digits is 9.
Let us assume the digit of units place be x.
Then the digit of tens place will be 9-x.
Thus the two digit number is 10(9-x) + x
Now if we reverse the digits, the number becomes 10x + (9-x).
As per the question,
10x + (9-x) = 10(9-x) + x + 27
or 9x + 9 = 90 - 10x + x + 27
or 9x + 9 = 117 - 9x
Transposing -9x to the LHS and 9 to the RHS:
9x + 9x = 117 - 9
or 18x = 108
x = 6
Thus two digit number is 36.
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