Answer:

the number is 56 .

Step-by-step explanation:

Let x be the unit digit of the number.

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 ,

When digits are interchanged ,unit digit=11−x and tens digit =x

When digits are interchanged ,unit digit=11−x and tens digit =xSo, number obtained by interchanging the digits= 10x+(11−x)=9x+11

When digits are interchanged ,unit digit=11−x and tens digit =xSo, number obtained by interchanging the digits= 10x+(11−x)=9x+11As per the question-

As per the question-9x+11−(110−9x)=9

As per the question-9x+11−(110−9x)=9⇒9x+11−110+9x=9

As per the question-9x+11−(110−9x)=9⇒9x+11−110+9x=9⇒18x+11−110=9

As per the question-9x+11−(110−9x)=9⇒9x+11−110+9x=9⇒18x+11−110=9⇒18x=9−11+110

As per the question-9x+11−(110−9x)=9⇒9x+11−110+9x=9⇒18x+11−110=9⇒18x=9−11+110⇒18x=108

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.

Hence, unit's digit = 6 and ten's digit = 11−6=5.Therefore, the required number is 56.

Verified answer

Step-by-step explanation:

The given number is less than the number obtained by interchanging the digits by 9. Therefore, (10x+y)−(10y+x)=9. Putting the value of x in x+y=11, we get y=11−x=11−6=5. The number was 56

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