 Hello and welcome to the session. I am Asha and I am going to help you with the following question which says, A farmer buys a used tractor for Rs 12,000. He pays Rs 6,000 cash and agrees to pay the balance in annual installments of Rs 500 plus 12% interest on the unpaid amount. How much will the tractor cost him? Let's now begin with the solution and total cost of used tractor is equal to Rs 12,000 and he pays Rs 6,000 cash, so cash down payment is equal to Rs 6,000. Therefore, amount to be paid in installments is equal to Rs 12,000 minus Rs 6,000 which is equal to Rs 6,000. Therefore, amount to be paid in installments is equal to Rs 6,000. Now let us find the first instalment paid by him which is equal to Rs 500% on the unpaid amount and the unpaid amount which is to be paid in installments is Rs 6,000. So, 12% of Rs 6,000, so this is equal to Rs 500 plus 12 upon 100 into 6,000 which is further equal to Rs 500 plus 720. So, this is equal to Rs 1200, 20. Therefore, the first instalment is of Rs 1200, 20. Now, let us find the second instalment equal to Rs 500 plus 12% of the unpaid amount which is Rs 5,500. Since after paying Rs 500, we will subtract Rs 6,000 minus Rs 500 to get the unpaid amount for the second instalment. This is equal to Rs 500 plus 12 upon 100 into Rs 5,500 which is further equal to Rs 500 plus Rs 660 which is further equal to Rs 1160. Now let us find the third instalment equal to Rs 100 plus 12% of the unpaid amount which we again get on subtracting Rs 500 from Rs 5,500 and that is Rs 5,000 which is further equal to Rs 500 plus 12 upon 100 into Rs 5,000 which is further equal to Rs 500 plus Rs 600 which is equal to Rs 1100. So, this is the third instalment and therefore, amount paid by the farmer instalments is equal to Rs 1220 plus Rs 1160 plus Rs 1100 plus so on and the number of instalments are 12 cents and multiplying 12 with Rs 500 we get Rs 6,000 which is the amount to be paid in instalments. Now, as we can see the instalments common AP whose first term that is denoted by A is 1220 and the common difference that is denoted by D is minus 60 and the sum of N terms of an AP is given by N upon 2 into 2 times of 8 plus N minus 1 into D. So, by using the sum of N terms of an AP let us find the sum of these instalments which are 12 in number. So, this will be equal to 12 upon 2 into 2 times of 1220 plus 12 minus 1 into minus 60 this is further equal to 26 or 12 6 into 2440 plus 11 into minus 60 which is further equal to 6 into 2440 minus 600 60 which is further equal to 6 into 1780 which we get on subtracting 660 from 2440 and this is equal to Rs 10,680 therefore, amount to the farmer for the tractor is equal to Rs 6,000 which he paid cash plus Rs 10,680 which he paid in instalments. So, this is equal to Rs 16,680. So, the total cost of the tractor which the farmer paid is Rs 1,600,680. So, this completes the session. Bye and take care.