 Hello and welcome to the session. Today I'll help you solve this question. The question says, some of the digits of a two digit number 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? Now let's see the solution. Let's assume that unit's digit v equal to x. Now since it's given in the question that some of the digits of a two digit number is 9, so we have the tens digit would be equal to 9 minus x. This can be shown with the help of an example. Like if sum of two numbers is 9 and one of the numbers is 5, then the other number would be equal to 9 minus 5. And now the two digit number would be equal to 10 multiplied by the tens digit that is 9 minus x plus the unit's digit that is x. And which is indeed equal to 10 multiplied by 9 plus 10 multiplied by minus x plus x. And this is equal to 90 minus 10x plus x which is equal to 90 minus 9x. Now when the digits are interchanged, tens digit would be equal to x and unit's digit would be equal to 9 minus x. And then the new number would be equal to 10 multiplied by the tens digit that is x plus the unit's digit that is 9 minus x. And this is equal to 10x plus 9 minus x equal to 9 plus 9x. Now according to the question we have, when we interchange the digits, it is found that the resulting new number is greater than the original number by 27. So according to the question we have, new number is equal to the original number plus 27. That is new number is 9x plus 9 equal to the original number 90 minus 9x plus 27. Now we transpose this negative 9x to the left-hand side we have 9x plus 9x plus 9 is equal to 90 plus 27 is 117. And now we transpose this positive 9 to the right-hand side so we have 9x plus 9x is 18x equal to 117 minus 9 which further implies 18x is equal to 108. Now to find the value for x we will divide both the sides by 18 so we have 18x upon 18 is equal to 108 upon 18. Now this 18 and this 18 gets cancelled and 6 times 18 is 108 so we have x is equal to 6. And thus we say that units digit is equal to 6, 10 digit is equal to 9 minus x equal to 9 minus 6 and that is equal to 3. So the number would be equal to 10 multiplied by 10 digit that is 3 plus units digit that is 6 and that is equal to 30 plus 6 equal to 36. Hence 36 is the required 2 digit number so final answer is 36. Hope you enjoyed the session have a good day.