Question

The number obtained by reversing a two digit number is 18 more than the original number. If the sum of its digits is 8 , find the number...

please explain and give the answer..

Answer 1

let the digit in the tens place be x and ones place be y.

Original no. =10x+y

sum of digits =>x + y= 8 --- (i)

Given=> When 18 is added to the original no. the new no. formed has the digits which are the same as the original no.'s but the digits have just interchanged their places so,

New no.= 10y + x

and

New no. is greater than original no. by 18 so,

10y + x -( 10x + y)=18

10y + x -10x -y=18

9y-9x = 18

9(y-x ) = 18

y-x=2 ----(ii)

adding (i) and (ii)

we have ,

x + y = 8

y - x = 2

---------------

2y = 10

y=5

now x + y = 8

substituting y as 5 we get

x + 5 = 8

x = 8-5

x = 3

Therefore the original number is 35.

Answer 2

I dont know how to solve this question