Question

The sum of the 2 digit number and number obtained by reversing the order of the digit is 132 , if 12 is added to the number the new number becomes 5 times the sum of the digits . Find new number.

Answer 1

Let the number be 10y+x i.e the digit at ten's place is y and that in one's place is x
given 10y+x + 10x+y=132 ---------1
also given 10y+x + 12=5(x+y) which gives 10y+x=5(x+y)-12 ---------2
sub. 2 in 1
5(x+y)-12+10x+y=132
solving the above equation for x, you will get x=(48-2y)/5 ------3
sub. 3 in 1
10y+ (48-2y)/5 + 10(48-2y)/5 +y=132
solving the above equation for y, you will get 33y=132 which gives y=4 --------4
sub. 4 in 3
you will get x=8
so the number is 10y+x= 10(4)+8=48