Question:
The difference between a 2-digit number and the number obtained by interchanging its digits is 63. What is the difference between the digits of the number?
Solution:
Let the tens place digit be 'x' and the units place digit be 'y'.
∴ Number = (10x + y)
Number obtained by interchanging the digits = (10y + x)
Given: (10x + y) - (10y + x) = 63
∴ 10x - x + y - 10 y = 63
9x - 9y = 63
9(x - y) = 63
x - y = 7
Therefore, the difference between the digits of the number is 7.
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