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 ?

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 ?
1). 64
2). 46
3). 96
4). 69

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Guest · Answer 1 · 2019-04-09 22:39:54

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

Guest · Answer 2 · 2019-05-08 12:23:22

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

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 ?

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