Question

Sum of a digit of a two digit is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two digit number ?

Answer 1

Answer:

36

Step-by-step explanation:

Let the unit digit be b and tens digit be a.

   Number should be ab or 10a + b.

  Given,

           Sum of digits is 9     ⇒ a + b = 9       ⇒ b = 9 - a

When digits are interchanged:

 New number is ba or 10b + a.

According to the condition:

⇒ New number = original number + 27

⇒ 10b + a = 10a + b + 27

⇒ 10b - b = 10a - a + 27

⇒ 9b = 9a + 27

⇒ 9b = 9( a + 3 )

⇒ b = a + 3                { value of b from above }

⇒ 9 - a = a + 3

⇒ 9 - 3 = a + a

⇒ 6 = 2a

⇒ 3 = a

           Thus,

          b = 9 - 3   ⇒ b = 6.

Thus,

  number is ab = 36.

Answer 2

☯️Answer:☯️

_______________________________

Let the digits in the tenth place be x.

And the digit in the ones place be y.

Then according to the question,

Sum of two digits =9

Then,

x+y=9_________equation 1

The original number be in the form 10x+y.

When the digits are interchanged then the number becomes, 10y+x.

So, as the resulting number is greater than the original number by 27. Therefore,

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

10y+x-10x-y=27

9y-9x =27

9(y-x)=27

$(y - x) = \frac{27}{9} = 3$

So, y-x =3________eq2

Now, from eq1 and eq2, we get

x+y=9

x=9-y_______eq3

Now using eq3 in eq 2 we get,

y-x=3

y-(9-y)=3

y-9+y=3

2y=3+9=12

y=12/2=6.

So, x =9-6=3.

Therefore, x=3 and y=6.

So, the number is 36.

_________________________________

$Be \: brainly$