Question

The sum of the digit of two-digit is 12. the number obtained by inter changing its digit exceeds by the given number 18.find the number

Answer 1

let the digit at units place be x
then digit at tens place = 12-x

value of unit digit = x
value of tens digit = 10(12-x) => 120-10x
therefore, the number => 120-10x+x
=> 120-9x

if digits are interchanged then
units digit = (12-x)
its value = 1(12-x) => 12-x

tens digit = x
its value = 10x

therefore ,the new number = 10x+12-x
=> 12+9x

according to question ,
120-9x = 12+9x+18
120-9x = 30+9x
120-30 = 9x+9x
90 = 18x
x= 90/18 => 5

therefore , the number => 120-9x => 120-9(5) => 120-45 => 75
or the number = 12+9x => 12+9(5) => 12+45 => 57

hope this helps

Answer 2

Let the number be xy.

The sum of the digit of two-digit is 12.

x+y = 12

the number obtained by inter changing its digit exceeds by the given number 18



10y+x -18=10x+y

==> 9y -9x = 18

==> x-y =-2

Now adding x + y =12, x-y =-2

2x =10

x =5.

5+y =12

y =7.

The number is 57.