 Hello and welcome to the session. In this session we discussed the following question which says the sum of the two digits of a number is 8. The digits gets reversed when 18 is added to the number, find the number. Let's move on to the solution now. We take let the 10th digit be equal to x. Now as given that the sum of the two digits is 8, so the 1st digit would be equal to 8 minus x. So the number formed with the 10th digit as x and the 1st digit as 8 minus x would be equal to 10 into the 10th digit that is x plus 1 into the 1st digit that is 8 minus x. This would be equal to 10x plus 8 minus x equal to 9x plus 8. Now consider the number formed when digits are reversed. This would be equal to 10 into 8 minus x plus 1 into x that is in place of the 10th digit we take the 1st digit and in place of the 1st digit we take the 10th digit. So this would be equal to 80 minus 10x plus x. This is equal to 80 minus 9x. Now according to the question we have that when 18 is added to the number then the digits get reversed. So when we add 18 to the original number that is 9x plus 8 this would be equal to the number formed when digits are reversed that is 80 minus 9x. This gives us 9x plus 26 is equal to 80 minus 9x. Now we transpose this term minus 9x from the right hand side to the left hand side. So we have 9x plus 9x plus 26 is equal to 80. Next we transpose 26 from left hand side to the right hand side. So we get 18x is equal to 80 minus 26. So we have 18x is equal to 54. This gives us x is equal to 54 upon 18. Now 18 3 times is 54. So we get x is equal to 3. So now the 10th digit is equal to 3 since we have taken the 10th digit to be equal to x. Now the 1st digit is equal to 8 minus x. So we have the 1st digit is equal to 8 minus 3 equal to 5. Now the number formed would be equal to 10 into the 10th digit plus 1 into the 1st digit. This is equal to 30 plus 5 equal to 35. So 35 is the final answer. This completes the session. Hope you have understood the solution for this question.