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 45.What is the two-digit number?
Question
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 45.What is the two-digit number?
Solution
Let's solve this step by step:
Step 1: Let's assume the two-digit number is XY, where X is the tens digit and Y is the units digit. According to the problem, X + Y = 9.
Step 2: When we interchange the digits, the number becomes YX. According to the problem, YX = XY + 45.
Step 3: We can express YX and XY in terms of X and Y. YX is actually 10Y + X, and XY is 10X + Y.
Step 4: Substitute YX and XY in the equation from step 2, we get 10Y + X = 10X + Y + 45.
Step 5: Simplify the equation, we get 9Y = 9X + 45.
Step 6: Divide the equation by 9, we get Y = X + 5.
Step 7: Substitute Y in the equation from step 1, we get X + X + 5 = 9, which simplifies to 2X = 4, so X = 2.
Step 8: Substitute X = 2 in the equation Y = X + 5, we get Y = 7.
So, the two-digit number is 27.
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