Question

The sum of the digits of a two digit number is 9.if the digits are interchanged the number obtained exceeds the original number by 27. what is the number?

Answer 1

Let the unit digit is x and tens digit is your then number be 10y+x X+y=9......... (1) Now 10x+y-10y-x=27 Or 9x-9y=27 Or 9 (x-y)=27 X-y=3...... (2) Adding equation 1 &2 X+y+x-y=9+3 Or 2x=12 X=6 Put the value of x in equation 1 X+y=9 6+y=9 Y=9-6=3 Required number be 10 ×3+6=36

Answer 2

Let the digit at ones place be x Tens place =9-x 10(9-x)+x=90-10x+x=90-9x 10(x)+(9-x)=10x+9-x=9x+9 90-9x+27=9x+9 63-9x=9x+9 63-9=9x+9x 54=18x 54/18=x X=3 Ones place = 3 Tens place =9x=9-3=6 Therefore number=63