 Hello and welcome to the session. Let us understand the following problem today. The students of a class are made to stand in rows. If three students are extra in a row, there would be one row less. If three students are less in a row, there would be two rows more. Find the number of students in the class. Now, before starting with the solution, let us see how we will find the 12th number of students. The total number of students is equal to number of students in a row multiplied by number of rows. And this is our key idea to the question. Now, let us start with the solution. Let the number of students equal to x and let the number of rows be y. Therefore, number of students in each row is equal to x divided by y. Now, let us consider case one. According to the question, when three students are extra in a row, then there would be one row less. Therefore, we have students is equal to x divided by y plus three and number of rows is equal to y minus one. Now, the number of students is equal to number of rows multiplied by number of students in each row. This is our key idea. That is, x is equal to y minus one multiplied by x by y plus three. Now, solving this, we get it implies x is equal to x plus three y minus x by y plus minus three. Now, we see that this and this gets cancelled. So, which implies x by y minus three y plus three is equal to zero. This is our equation one. Now, case two. If three students are less in a row, there would be. Therefore, we have students becomes x by y minus three. Number of rows is equal to y plus two. That is two rows more. That is now our equation becomes total number of students. That is x is equal to number of rows. That is y plus two multiplied by number of students in each row. That is x by y minus three. This is by key idea we have got. Now, solving this, it implies x is equal to x minus three y plus two x by y minus six. Which implies this and this gets cancelled. So, we are left with two x by y minus three y minus six is equal to zero. This is our equation two. Now, we have got the two equations and they are x by y minus three y plus three is equal to zero as equation one. And two x by y minus three y minus six is equal to zero as equation two. Now, let x by y is equal to u. Therefore, we get u minus three y is equal to minus three as equation four. So, I three and two u minus three y is equal to six as equation four. Now, solving these equations three and four, we get all subtracting. Now, do not forget to claim these signs while subtracting. This gets cancelled. So, we get this u minus two u gives minus u which is equal to minus three minus six is equal to minus nine. Now, this and this gets cancelled. So, which implies u is equal to nine. Now, therefore, x by y is equal to nine because we have assumed u is equal to x by y. So, which implies x is equal to nine y. Substituting u is equal to nine in equation three, we get nine minus three y is equal to minus three. Which implies minus three y is equal to minus three minus nine. Which implies minus three y is equal to minus twelve. This gets cancelled. So, this implies y is equal to four and x is equal to nine y. So, since x is equal to nine y, therefore, x is equal to nine multiplied by four. Which implies x is equal to thirty six. Therefore, the number of students is equal to thirty six. This is our required answer. I hope you understood the problem. Bye and have a nice day.