Sum of the digits of a two digit number is 12. If the digit of the number are inter changed, then the new number is 36 less than the original number. What is the original number?

Solution(By Examveda Team)

Method 1:
Let x = the 10's digit
Let y = the units
10x + y = the original two digit number
The sum of the digits of a two-digit number is 12.
x + y = 12 -------(i)

"If the digits are reversed, the number is 36 less than the original number."
Reverse no. = original no. - 36
10y + x = 10x + y - 36
10y - y = 10x - x - 36
9y = 9x - 36
simplify, divide by 9
y = x - 4
x - y = 4 ------(ii)

Now Resolving equation (i) and (ii) x = 8 and y =4;
Therefore Original number is 84

Method 2(short cut method):
X + Y = 12 and X - Y = (difference between original and reversed number)/9
i.e X - Y=4
Therefore Original number is 84