Question

CSATEasyPrelims 2017Maths

There are certain 2-digit numbers. The difference between the number and the one obtained on reversing it is always 27. How many such maximum 2-digit numbers are there?

Explanation

Step 1: Define the Number and Its Reverse: Let the number be $10x + y$ , where: $x$ = tens digit $y$ = ones digit The reverse is $10y + x$ .

Step 2: Set Up the Equation: The difference between the number and its reverse is given by: $(10x + y) - (10y + x) = 27$ Simplifying the equation: $9x - 9y = 27$ $x - y = 3$

Step 3: Solve for Possible Values of x and y: The equation $x - y = 3$ implies: Possible pairs of $(x, y)$ are: $(4, 1)$ $(5, 2)$ $(6, 3)$ $(7, 4)$ $(8, 5)$ $(9, 6)$

Step 4: List the Corresponding Numbers: The corresponding two-digit numbers are: $(4, 1) \rightarrow 41$ $(5, 2) \rightarrow 52$ $(6, 3) \rightarrow 63$ $(7, 4) \rightarrow 74$ $(8, 5) \rightarrow 85$ $(9, 6) \rightarrow 96$