Question

The sum of a two digit number and the number formed by reversing its digits is 132.If the difference of the digits is 2,find the number.
answer-75 just need step by step formula​

Answer 1

Answer:

The number is 75.

Step-by-step explanation:

Let the 2 digits be x and y respectively

2 digit number be$=10x+y$

2 digit number obtained by reversing the digit$=10y+x$

The sum of a two digit number and the number formed by reversing its digits is 132.

           $10x+y+10y+x=132\\ \\ 11x+11y=132\\ \\ x+y=12----(1)$

The difference between  the two digits is 2.

$x-y=2----(2)$

Adding equation (1) and (2) ,

                $x+y+x-y=12+2\\ \\ 2x=14\\ \\ x=\frac{14}{2}=7$

Putting the value of x in equation (1)

                                    $x+y=12\\ \\ y=12-x\\ \\ y=12-7\\ \\ y=5$

Number

                     $=10x+y=10 \cdot 7+5\\ \\ =70+5=75$