 Hello and welcome to the session let's work out the following problem. It says a two-digit number is said that the product of X digits is 35. When 18 is added to the number the digits interchange their places, find the number. So let's now proceed on with the solution. We have to find a two-digit number. So let the digit units place Y and let the digit displace. Therefore the given number is given by 10X plus Y. As we know that any two-digit number is given by 10 into the digit at 10's place plus the digit at units place. For example if we have a number say 25 the same digit is 10 into 2 plus 5 and that gives us exactly 25. So now we are given that the product of X digits is 35. So according to question of digits is 35 that is X into Y is equal to 35. Let's name this as 1 and we are given that when 18 is added to the number the digits interchange their places. That means the digit at 10's place goes at units place and the digit at units place comes at the 10's place. Right? So we have we add 18 to the given number then if we add 18 to the given number the digits interchange their places that means Y comes at the 10's place and X goes at the units place. So the number becomes 10Y plus X. Right? So this implies 10X plus Y plus 18 minus 10Y minus X is equal to 0 and this implies 9X minus 9Y plus 18 is equal to 0 taking 9 common we have X minus Y plus 2 is equal to 0. Let's name this as 2. Now from 1 we have Y is equal to 35 upon X so put Y is equal to 35 upon X into so we have X minus 35 upon X plus 2 is equal to 0 that is the LCM. So we have X square minus 35 plus 2X is equal to 0 and this implies X square plus 2X minus 35 is equal to 0. Now this is a quadratic equation in X and we'll solve this quadratic equation for X so we factorize X square plus 7X minus 5X minus 35 is equal to 0 taking X common from the first two terms we have X into X plus 7 taking minus 5 common from the last two terms we have minus 5 into X plus 7 is equal to 0 and this implies X plus 7 into X minus 5 is equal to 0. So this implies X plus 7 is equal to 0 or X minus 5 is equal to 0 and this implies X is equal to minus 7 or X is equal to 5. Now when X is equal to minus 7 Y is equal to 35 upon X and which is minus 7 so this is equal to minus 5 and we have obtained the value of Y using this let's name this as A and when X is equal to 5 then Y is equal to 35 upon 5 which is equal to 7 again using A therefore the given number into minus 7 plus minus 5 and this is equal to minus 75 or into 5 plus 7 because the given number is NX plus Y so in this case it becomes 57 hence the given number is either minus 75 or 57 so just completes the question and the session bye for now take care have a very nice day