Question

sum of the digits of a two digit number is 9 the number obtained by interchanging the digits exceeds the given number by 27 find the given number

Answer 1

Given data

=> x + y = 9; yx = xy + 27

To get 9 as sum the combination of x an y can be used only between 1 an 9.

1 + 8, 2 + 7, 3 + 6, 4 + 5, 5 + 4, 6 + 3, 7 + 2, 8 + 1

Looking at the above combinations the correct combination can be seen for the combination x = 3, y = 6

=> x + y = 3 + 6 = 9;  xy = 26

=> xy + 27 = 36 + 27 = 63

Here 63 is obtained by interchanging 36.

∴The actual number is 36.

Answer 2

Given data

=> x + y = 9; yx = xy + 27

To get 9 as sum the combination of x an y can be used only between 1 an 9.

1 + 8, 2 + 7, 3 + 6, 4 + 5, 5 + 4, 6 + 3, 7 + 2, 8 + 1

Looking at the above combinations the correct combination can be seen for the combination x = 3, y = 6

=> x + y = 3 + 6 = 9;  xy = 26

=> xy + 27 = 36 + 27 = 63

Here 63 is obtained by interchanging 36.

∴The actual number is 36.