 Hello and welcome to the session. In this session we discussed the following question which says a two digit number is 12 more than 4 times the sum of its digits. If 9 is subtracted from the number the digits are reversed. Find the number. We need to find a two digit number such that it is 12 more than 4 times the sum of its digit and also the digits would be reversed if we subtract 9 from the number. So let's see how we can find this number. First of all we assume let the 10 digit of the required number be x and also we assume the unit digit of the required number be y. So the number formed with x as the 10 digit and y as the units digit is equal to 10 into the 10 digit that is x plus the units digit that is y. So the number formed is equal to 10 x plus y. Now the sum of the digits is equal to x plus y that is the 10 digit plus the units digit. Now according to the question we have that the two digit number is 12 more than 4 times the sum of its digit. So the number formed that is 10 x plus y is equal to 4 times x plus y that is the sum of the digits plus 12 since it is 12 more than 4 times the sum of its digit. So this further gives us 10 x plus y is equal to 4 x plus 4 y plus 12 that is 10 x plus y minus 4 x minus 4 y is equal to 12. Now from here we have 6 x minus 3 y is equal to 12. Now taking 3 common here we get inside the bracket 2 x minus y is equal to 12. Now this further gives us 2 x minus y is equal to 12 upon 3 that is equal to 4. So we take this as equation 1. Now let's see what would be the number formed by reversing the digits this would be equal to 10 y plus x. Now since we have taken x to be the 10 digit and y to be the units digit now when we interchange the digits or we reverse the digits we take y as the 10 digit and x as the units digit so the new number formed would be 10 y plus x. We are given one more condition in the question so according to the question we have that if we subtract 9 from the given number the digits would be reversed. So our original number was 10 x plus y thus when we subtract 9 from the number 10 x plus y the digits would be reversed and this would be equal to the number formed by reversing the digits that is 10 y plus x. This gives us 10 x plus y minus 9 is equal to 10 y plus x whether we have 10 x plus y minus 10 y minus x is equal to 9 or you can say we have 9 x minus 9 y equal to 9 this gives us x minus y is equal to 1. So we take this as the second equation so now we have got two equations one is 2 x minus y equal to 4 and x minus y equal to 1. Now we will solve these two equations to get the values for x and y for this we subtract equation 2 from equation 1 so subtracting 2 from 1 we get 2 x minus y minus x minus y is equal to 4 minus 1 that is 2 x minus y minus x plus y is equal to 4 minus 1 this further gives us x is equal to 3. Now we have got the value for x now substituting x equal to 3 in equation 2 we get 3 minus y equal to 1 this gives us minus y is equal to 1 minus 3 we have minus y is equal to minus 2 so this gives us y is equal to 2 thus the values for x and y are x equal to 3 and y equal to 2 so the required number is equal to 10 into x plus y this is equal to 30 plus 2 is equal to 32. So 32 is the required number so this completes the session hope you have understood the solution for this question.