Question

The sum of a two digit number is 9. If 27 is added to the number , the digits are reversed. Find the number.

Answer 1

let the number be xy
x+y=9...............(1)
(10x+y)+27=10y+x
10x-x+y-10y=-27
9x-9y=-27
x-y=-3................(2)
add equation 1 and 2
we get
x=3
substitute it in eq 1
y=6
so the number is 36

Answer 2

Answer:

Let the digit at unit's place be y and the digit at ten's place be x.

So, the number will be 10x+y

According to the first condition-

⇒x+y=9    ....(1)

According to the second condition-

⇒10y+x=10x+y+27⇒9y=9x+27

⇒y=x+3    ...(2)

Put the value of y in (2), we have

⇒x+x+3=9

⇒x=3

⇒x+y=9

⇒3+y=9

⇒y=6

∴ the number is 36