 Hello and welcome to the session. The given question says a two digit number is such that the product of its digits is 15. If 18 is added to the number then the digits interchange their places. Find the number. Let's start with the solution and let the units digit of the number be x and the tenth digit of the number be equal to y. Therefore, the required number is equal to 10 into y plus x since y is in the tenth place and x is in the one's place. So we multiply y by 10 and x by 1 to get the number and then we add them. Right? Now the question says a two digit number is such that the product of its digit is 15. So first does x into y is equal to 15. The digits are x and y so their product is equal to 15. Then there is the equation number 1. Now the question further says if 18 is added to the number according to the question we have when we add 18 to the number that is 10 y plus x plus 18 the digits interchange their places. So y becomes the units digit and x comes to the tenth place. So the new number will be 10 x plus y where 10 x plus y is the number obtained after entertaining the digits. Now simplifying it further we have taking all the variables on the left hand side we have 9 y minus 9 x is equal to minus 18 or we have x minus y is equal to 2. Let this be equation number 2. Now let us solve equation 1 and 2 for the values of x and y. Now from 1 we have that y is equal to 15 divided by x. So substituting y is equal to 15 divided by x in equation number 2 it implies that x minus 15 divided by x is equal to 2 or we have x square minus 2x minus 15 is equal to 0. Now we are splitting the middle term it can further be written as x square minus 5x plus 3x minus 15 is equal to 0. Now taking x common from the first 2 terms and 3 common from the last 2 terms we have x into x minus 5 plus 3 times of x minus 5 is equal to 0 or we have x minus 5 into x plus 3 is equal to 0 and this further implies that either x minus 5 is equal to 0 or x plus 3 is equal to 0. Since we know that if the product of two numbers is equal to 0 then at least one of them is 0 so this implies either a is equal to 0 or we have b is equal to 0. So this further implies that x is equal to 5 or minus 3. Now the digits cannot take the negative values so rejecting minus 3 we have x is equal to 5. Now we are given that product of the digits x into y is equal to 15 so this implies y is equal to 15 divided by x or 15 divided by 5 which is equal to 3. Therefore x is equal to 5 and y is equal to 3 and thus the required number which is equal to 10y plus x is equal to 10 times of 3 plus 5 is equal to 30 plus 5 thus gives 35. Hence the required number is 35. So this completes the session. Hope you have understood it. Bye and take care.