Question

Sum of 2 digit number is 9 if we interchange the digits the resultant number is greater by 27

Answer 1

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

According to first condition :

x+y =9. -(I)

According to second condition :

10y+x=10x+y+27

10y-y+x-10x=27

9y-9x=27

9(y-x)=27

Y-x=3. -(ii)

Add (I) and (ii)

X+y=9

-x+y=3

2y=12

Y=6

Hence;x=9-y

X=9-6

X=3

Hence,required number is 10x+y

which is equal to 10(3)+6

i.e 36