Question

sum of the digits of a 2 digit number is 11. the given number obtained by interchanging the digit by 9 . find the number.
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Answer 1

Answer:

The number can be 56 or 65 ans.

Step-by-step explanation:

Let's assume the numbers :

x (tens place) and y (ones place)

Their sum is 11

so, x + y = 11 ........ (i)

The number formed :

➡ 10x + y

Again, interchanging of digits the number formed :

➡ 10y + x

$\sf : \implies \:( 10x + y) - (10y + x) = 9\\ \sf : \implies \:10x + y - 10y - x = 9\\ \sf : \implies \:9x - 9y = 9\\ \sf : \implies \:x - y = 1.....(ii)$

Now,we have equations :

➡ x + y = 11 ......... eq. (i)

➡ x - y = 1............eq.(ii)

Substraction of both the equation :

$\sf \: x + y = 11 \\ {\sf {\underline{x - y = 1}}} \\ : \sf \implies \: 2x = 10\\ \sf : \implies \:x = 5 \: ans.$

Substituting the value of x in equation (i) :

x + y = 11

5 + y = 11

y = 6

Hence,

The number can be 56 ot 65.

Answer 2

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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