Question

A number is 27 more than the number obtained by reversing its digits. If its unit's and ten's digit are x and y respectively, write the linear equation representing the above statement.

Answer 1

Given, unit's digit = x

and tens digit = y

$\therefore$ Number = x + 10y

By reversing the digits, units digit = y

and ten's digit = x

$\therefore$ number = y + 10x

Now difference of these two numbers = 27

$(x+10y)-(y+10x)=27\Rightarrow x+10y-y-10x=27\Rightarrow -9x+9y-27=0\Rightarrow x-y+3=0(\text{Dividing~by}-9)\text{Hence equation is}x-y+3=0$