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sum of the digits of a two digit number is 9 when when we interchange the digits it is found that the resulting new number is greater than t

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sum of the digits of a two digit number is 9 when when we interchange the digits it is found that the resulting new number is greater than t

Question

sum of the digits of a two digit number is 9 when 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 ?

## Answers ( )

Answer:The sum of the two digits is 9.

On interchanging the digits, the resulting new number is greater than the original number by 27.

Let us assume the digit of units place be x.

Then the digit of tens place will be 9-x.

Thus the two-digit number is 10(9-x) + x

Let us reverse the digit

the number becomes 10x + (9-x).

As per the given condition

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

= 9x + 9 = 90 – 10x + x + 27

= 9x + 9 = 117 – 9x

On rearranging the terms we get,

=18x = 108

x = 6

So the digit in units place is 6

Digit in tens place is 9-x= 9-6=3

Hence the number is 36✔Answer:Therequiredtwo digitnumberis36Step-by-step explanation:Let the unitdigitbe y and tens digit be xSotheNumber= 10x + yNowtheReversenumberobtainedinterchangingthe digits= 10y + xNowby thegivenconditionx + y = 9…………………………(1)And10y + x = 10x + y +27…………………….(2)9y – 9x = 279y – 9x = 27y – x =3……………………………………..(3)AddingEquation(1)andEquation(3)we get2y=12y = 6Sox=9–6=3HenceOriginal Number = 36