The digits of a two-digit numbers are in the ratio 2:3 and the numbers obtained by interchanging the digits is greater than the original number by 27. What is the original number?
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let the digits are 2x and 3x .
If 2x is unit-place digit and 3x is tenth-place digit, then the number is (3x)10+2x = 32x
By reversing the digits, number obtained is (2x)10 + 3x = 23x
Since the difference is 27, we have 9x = 27 or x = 3
hence digits are 6 and 9 and original number is 69
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