Question

the sum of a two digit number is 15.if the number formed by reversing the digits is less than the orginal number by 27, find the orginal number.

Answer 1

let the number be x
then the digit in tens place be 15-x,
therefore,10(15-x)+x=150-10x+x
=150-9x
number obtained by reversing digits=10x+15-x
                                                         =9x+15
it is given that 27 is subtracted so
frm first eqn;
150-9x-27=reversed number
                =9x+15
123-9x=9x+15
-18x=-108
x=6
by substituting value of x in 150-9x
150-9*6=150-54=96

Answer 2

Let the 10 digit number be x
Let the one digit number be y
x + y = 15
y = 15 - x 
Original number = 10x + y
Reversed number = 10y + x
10y + x = 10x + y - 27
10(15-x) + x = 10x + 15 - x - 27 (Substituting y)
150 - 9x = 9x - 12
18x = 162
x = 9
y = 15 - 9
y = 6
Therefore, the 10 digit number is 9 and the one digit number is 6, and the original number is 96.