 Hello and welcome to the session. Let's work out the following problem. It says the sum of two digit number and the number obtained by reversing the order of its digits is 165. If the digits differ by 3, find the number. So, let's now move on to the solution. We have to find a two digit number. So, let the digit units place 10th place digit BY. Therefore, the original number or the given number is 10Y plus X as we know that any two digit number can be written as 10 into digit at 10th place plus the digit at units place. Now the number obtained by reversing the order of the digits at a reverse number will be 10X plus Y. That means the digit at units place comes at 10th place and the digit at 10th place goes at units place and we are given that the sum of the two digit number and the number obtained by reversing the order of its digits is 165. So, according to question, we have 10Y plus X plus Y is equal to 165. That is 11X plus 11Y is equal to 165. Now taking 11 common from both sides, we have X plus Y is equal to 15. Let us name this as Equation 1. Now we are given that digits differ by 3. That means the difference of the digit at units place and the digit at 10th place is equal to plus minus 3. Since we are not given that the digit at units place minus the digit at 10th place is equal to 3 or the digit at 10th place minus the digit at units place is equal to 3. So, we have written this as X minus Y is equal to plus minus 3. So, from this we have two cases that is X minus Y is equal to 3 or X minus Y is equal to minus 3. Let us name this as Equation 2 and let us name this as Equation 3. Now we will solve these for X and Y and first of all we will solve Equation 1 and 2 for X and Y. So, we have Equation 1 as X plus Y is equal to 15. Equation 2 as X minus Y is equal to 3. Now we will add Equation 1 and 2. Now since we are adding, so we have X plus X is 2X plus Y gets cancelled with minus Y. 15 plus 3 is 18. So, we have 2X is equal to 18 and this implies X is equal to 18 by 2 that is 9. Now we will put X is equal to 9 in any one of these two equations. So, we have put X is equal to 9 in 1. So, we have 9 plus Y is equal to 15. So, this implies Y is equal to 15 minus 9. So, this implies Y is equal to, so from this we have number is 10Y plus X. Now X is 9 and Y is 10. So, we have 10 into 6 plus 9. So, this is equal to 69. Now we will solve 1 and 3 and we will. So, we have X plus Y is equal to 15 and X minus Y is equal to minus 3. Now X plus X is 2X plus Y gets cancelled with minus Y and 15 minus 3 is 12. So, this implies X is equal to 12 by 2 that is 6. Now put X is equal to 6 in 1. So, we have 6 plus Y is equal to 15. So, this implies Y is equal to 15 minus 6. So, this implies Y is equal to 9. Therefore, the number is 10Y plus X that is 10 into 9 plus 6 and this is 96. So, the given number is either 69 or 96. So, this completes the question and the session. Bye for now. Take care. Have a good day.