Question

The sum of the digits of a two digit number is 8 and the difference between the number and that formed by

reversing the digits is 18. Find the number.​

Answer 1

Answer:

let the 2-digit number be xy,

according to given condition,

x+y= 8--------------------equation1

now according to the second condition,

yx - xy= 18-----------------equation2

as xy is a 2 digit number therefore it can be written in the form of (10x+y)...........x at tens place and y at ones place

similarly, yx is (10y+x)

puting in equation 2

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

10y + x - 10x - y = 18

9y-9x=18

9(y-x)=18

y-x=18/9

y-x=2-------------------equation 3

adding equation 1 and 3

therefore, (x+y)+(y-x)= 8 +2

x + y + y - x = 10

2y= 10

y=5

putting value of y in equation 2

y-x=2

5-x=2

x= 5 - 2

x= 3

therefore the 2 digit number is either xy= 35 or yx= 53