Question

sum of the digit of a two digit number is 9. when we intehange the digit it is found that the resulting new number great than the original number by 27 what is the two digits number.​

Answer 1

Conditions given in the Question:-

• Sum of digits=9
• Interchanging the digits, the resulting number is greater than orignal number by 27

______________

Solution:-

Let the first digit be x

Second digit=9-x. [As the sum of digits is 9]

So, orignal number= 10x+(9-x)

Interchanging the digits of the number= 10(9-x)+x

According to the Question,

• Interchanging the digits, the resulting number is greater than orignal number by 27

So let's make an equation according to this statement

Resulting Number-Orignal Number=27

{10(9-x)+x}-{10x+(9-x)}=27

=> (90-10x+x)-(10x+9-x)=27

=> (90-9x)-(9x+9)=27

=> 90-9x-9x-9=27

=> 81-18x=27

=> 81-27=18x

=> 54=18x

$\implies \sf\frac{54}{18} = x \\ \implies \sf 3 = x$

So we found the first digit of the original number i.e. 3

Second digit of the original number =9-x =9-3 =6

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Correct Answer:-

Orignal number=10x+(9-x)

= 10×3+6

= 30+6

= 36

Resulting number (after interchanging the digits)= 63

_______________

Verification:-

• Given, sum of the digits= 9

Check:-

3+6=9

9=9

• Given, after interchanging the digits, the resulting number is greater than orignal number by 27

Check:-

Resulting number=63

Resulting number-27=Orignal number

63-27=36

36=36

Since, Both the conditions are true, The answer is verified.

Answer 2

Answer:

The original number is 36

Step-by-step explanation:

Let the 2 digit number be 10x+ y.

x+ y =9 ....(i)

On interchanging the digits the number becomes = 10y + x

Resulting number = 10y+ x

Original number = 10x + y

According to the ques :-

10y + x - (10x + y) = 27

10y + x - 10x - y = 27

9y - 9x = 27

9( y-x)= 9× 3

y- x = 3......(ii)

Solving eqns (i) and (ii) :-

2y = 12

y= 6

And x = 9- y => x= 3

Since, Original number = 10x+ y

= 36 (Ans