 Hello friends, welcome to the session. I am Alka. Today we are going to solve the problem on the basis of pair of linear equations in two variables. Our question is, a lending library has a fixed charge for first three days and an additional charge for each date thereafter. Sarita paid Rs. 27 for a book, kept for seven days, while Suzy paid Rs. 21 for the book, she kept for five days. Find the fixed charge and the additional for each extra day. Here we see that we have to find two things, fixed charge and the extra charges, charge for each extra day. Let the fixed charge for first three days be Rs. x and let the additional charge for each extra day is equal to Rs. y. Therefore, charge for four extra days, charge for four extra days is equal to four y and charge for two extra days is equal to two y. Now we see from question that Sarita paid Rs. 27 for seven days that is four days extra. Now according to the question, Sarita paid Rs. 27 for seven days that is four extra days. So it can be written as therefore x which was a fixed charge for three days plus she had a book for four extra days which is four y is equal to 27. This is our first equation. Now we see from the question that Suzy paid Rs. 21 for five days that is two days extra. Therefore it can be written as x plus two y is equal to 21. This is our second equation. Hence the two equations are x plus four y is equal to 27, x plus two y is equal to 21. Now we see that on subtracting equation second from equation first we get our equations are x plus four y is equal to 27, x plus two y is equal to 21. We get this is plus, this is minus, minus, minus. These will get cancelled out. Four y minus two y is two y. 27 minus 21 will give us three. This implies two y is equal to six which can be written as y is equal to three. Hence now on substituting the value of y is equal to three in equation number one we get our equation first is x plus four y is equal to 27. Now we place the value of y here, x plus four into three is equal to 27 which gives us x plus 12 is equal to 27. This implies x is equal to 27 minus 12 which gives the value of x is equal to 15. Hence we see the equations are x plus four y is equal to 27 and x plus two y is equal to 21. Where x is the fixed charge and y is the extra charge for each day and the value of x is 15. This implies fixed charges are rupees 15 and extra charges for each day are rupees three. Hope you understood the solution and enjoyed it. See you. Goodbye and take care.