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Question 108
The digits of a two-digit number are in the ratio of 2 : 3 and the number obtained by interchanging the digit is bigger than the original number by 27. What was the original number ?
Solution
Let the two digit number be XY. So, the value of the number equals 10X+Y
When the digits are interchanged, the number becomes YX. So, the value of the number equals 10Y+X
From the information given, we know that X:Y = 2:3 and (10Y+X)-(10X+Y) = 9Y-9X
Hence, 9Y-9X = 27 or Y-X = 3
So, 3X=2Y and Y-X =3.
Solving both the equations, we get X=6 and Y=9.
So, the original number is 69
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