Question

A number consists of two digits whose sum is 9. If 27 is subtracted from the number its digits are reversed. Find the number.

Answer 1

x and y = 9
27 - 72 = 45
x = 45
y = 9

Answer 2

Let the number be xy (not x*y , it is xy like 65 which is not 6*5).
x+y=9
⇒x=(9-y)
Value of the number=10*x+y=10x+y.
Number when digits are reversed=yx.
Value of this number=10y+x.
Given,10x+y-27=10y+x
Putting x as 9-y we get
10(9-y)+y-27=10y+9-y
⇒90-10y+y+27=9y-9
⇒117-9y=9y-9
⇒117+9=9y+9y
⇒y=126/18=7.
x=9-7=2.