Question

the sum of two digit no.is 12. the number obtained by interchanging the two didit exceed the given number by 18. find the number.

Answer 1

Let the digits be x and y and let the tens digit be x and units digit be y.

Then, the number is 10x + y.

Given, x + y = 12 ------------- 1

On interchanging the digits, we get

10y + x.

10y + x exceeds the original number by 18. This gives

10y + x = 10x + y + 18

or 9y-9x = 18 or

y-x = 2 ------------------ 2

Adding equations 1 and 2, we get

y - x + x + y = 14

or 2y = 14

Therefore, y = 7

and x = y-2 = 7-2 = 5.

Therefore, the number is 5*10 + 7 = 57.