Question

In a two digit number the sum of two digit is 8.If 18 is added to the number its digit are reversed .Find the number.

Answer 1

ok, so our number is xy, which means 10x+y. 

Anyway, the first sentence say the sum of the 2 digits is 8, so x+y = 8 

if we add 18 to the number, ie 10x+y+18 the result is then yx (ie 10y+x)
--> 10x+y+18 = 10y+x
--> 9x + y + 18 = 10y


--> 9x - 9y + 18 = 0
--> 9x - 9y = -18
--> x - y = -2 

So we have 2 equations:
x+y=8
x-y=-2 

solve these to give x=3 and y=5 ie we had 35 and

Answer 2

35 is the answer
3+5=8
35+18=53 which is reverse of 35