 Hello and welcome to the session. In this session we discussed the following question that says the sum of the digits of a two digit number is 9. The number obtained by interchanging the digits exceeds the original number by 45, find the original number. Let's proceed with the solution now. We are given that the sum of the digits of a two digit number is 9 and we are also given one more condition according to which the number obtained by interchanging the digits exceeds the original number by 45 and we are supposed to find the original number. So first of all we assume let the tens digit be equal to x and let the ones digit be equal to y. So the original number in which the tens digit is x and the ones digit is y would be equal to ten multiplied by the tens digit that is x plus the ones digit that is y. That is the original number is ten x plus y. Now the new number obtained by reversing the digits is given by ten y plus x. That is we have interchanged the tens digit and the ones digit. Now let's see what are the conditions given to us in the question. So according to the question we have that the sum of the digits is 9 and the digits are x and y. So our first condition would be x plus y is equal to 9. Let this be equation one. Now the other condition given to us is that the new number that is the number which is obtained by interchanging the digits exceeds the original number by 45. That means that the new number ten y plus x is equal to the original number that is ten x plus y plus 45. So this means we have ten y plus x minus ten x minus y is equal to 45. Or you can say we have 9 y minus 9 x is equal to 45. Now taking out nine common from here we have y minus x is equal to 45. Or further we have y minus x is equal to 45 upon 9 and 9 5 times is 45. So we get y minus x is equal to 5 or minus x plus y is equal to 5. Let this be equation two. So thus now we have two equations minus x plus y equal to 5 and x plus y equal to 9. So we can easily solve these two equations to get the values for x and y. For this we add the two equations. So adding equations one and two we get minus x plus y plus x plus y is equal to 5 plus 9. This x cancels with minus x, y plus y is 2 y is equal to 9 plus 5 is 14. So to get the value for y we divide both sides by 2. Here 2 cancels with 2 and 2 7 times is 14. So we have y is equal to 7. Now we can find out the value of x by substituting y equal to 7 in equation one. So we have x plus 7 is equal to 9. This means that x is equal to 9 minus 7. So we have x is equal to 2. Thus we have got the values for x and y. Now the original number is given as 10x plus y. So we will substitute the values for x and y here to get the original number. So this is equal to 10 multiplied by 2 plus 7. This is equal to 27. So this is our original number that we were supposed to find out. So 27 is our final answer. This completes the session. Hope you have understood the solution of this question.