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

Answer:

The required no is 56 . How loook at the following steps

Step-by-step explanation:

Answer

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.

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Answer 2

Answer:

The number is 56

Step-by-step explanation:

Let the number be 10x + y

Therefore,

x + y = 11 .... (1)

10x + y + 9 = 10y + x

9x - 9y = -9

x - y = -1 .... (2)

Adding (1) and (2)

2x = 10

x = 5

Thus,

y = 6

Therefore,

The given number is 10x + y = 56