Your Answer is 84
Let x = the 10's digit, and y = the units digit
Write an equation for each statememt
"sum of the digit of two digit no. is 12."
x + y = 12
or
y = 12 - x; we use this for substitution, if needed
"the given no. exceed the no. obtained by interchange the digit by 36."
Given number: 10x + y
interchanged number: 10y + x
The equation from the given statement:
10x + y = 10y + x + 36
Some simple algebra:
10x - x = 10y - y + 36
9x = 9y + 36
Simplify, divide equation by 9
x = y + 4
Substitute (12-x) for y, (from the 1st statement)
x = (12-x) + 4
x + x = 12 + 4
2x = 16
x = 8
y = 12 - 8 = 4
Our number is 84:
Check it: 84 - 48 = 36
