Question

11. Sum of the digits of a two digit number is 12. the given number is 36 more than the number obtained by interchanging the digits. Find the given number.

Answer 1

here is your answer . answer is 84 you can see the solution in this photo

Answer 2

let the tens place be x and units place be y
therefore the original no. = 10x + y
according to condition,
sum of digit of two digit no. is 12
therefore x + y = 12 - - - 1.
according to second condition
the given no. is 36 more than the no. obtained by interchanging the digits,
10x + y + 36 = 10y + x
10x - x + y -10y = - 36
9x - 9y = - 36
dividing by 9 we get,
x - y = -4 - - - - 2.
adding both equation 1. and 2.

x+y = 12
+ x-y = -4
= 2x = 8
therefore x= 8 ÷ 2 = 4
put the value in equation 1.
x + y = 12
4 + y = 12
y = 12 - 4 = 8
therefore the no. is 48 which after interchanging becomes 84 and it's sum is also 12