Question

The sum of the digit of a two digit number is 12 The numbet obtained by interchanging the two digits exceeds the givem numbers by 18 Find the number.

Answer 1

let the number be 'xy' and x+y=12 and yx -xy=18

so let us write the possibilities 57,66,48,39

now only 57 satisfies the conditions
5+7=12. 75-57= 18

so answer is 57

Answer 2

Let the two digits be x and y,
x + y=12 ------@equation1
as the whole digit is in tens place so that,
10x+y=(10y+x) +18
10x+y=10y+x+18
10x-x = 10y-y +18
9x = 9y +18
9x -9y =18
x-y =2--------@equation2
so from equation 1 and 2,by eliminating method
x+y=12
x-y=2
-----------
2x=14
x=7
put this value in equation 1
x+y=12
7+y=12 (as x=7)
y=5
so that,
the no.is either 10x+y or 10y +x
10×7+5 or 10×5+7
75 or 57