Question

Sum of the digits of a two digit number is 11. The given number is less than the number obtained by interchanging the digits by 9. Find the number.​

Answer 1

Let x be the unit digit of the number.

Then, the ten's digit = 11−x

Therefore, Number = 10(11−x)+x=110−10x+x=110−9x

When digits are interchanged ,

unit digit=11−x and tens digit =x

So, number obtained by interchanging the digits= 10x+(11−x)=9x+11

As per the question-

9x+11−(110−9x)=9

⇒9x+11−110+9x=9

⇒18x+11−110=9

⇒18x=9−11+110

⇒18x=108

⇒x=6

Hence, unit's digit = 6 and ten's digit = 11−6=5.

Therefore, the required number is 56.