 Hello and welcome to the session, let's work out the following problem. It says a man repays a loan of Rs. 3,250 by paying Rs. 20 in the first month and then increases the payment by Rs. 15 every month. How long it will take to clear the loan? So let's now move on to the solution. We have to find the number of months in which the loan gets clear. So let the loan be cleared in n months. Now we are given that the first installment of the loan is Rs. 20 and then he increases the payment by Rs. 15 every month. So the second installment is Rs. 20 plus 15 that is 35 and so on he increases the payment by Rs. 15 every month. So these installments form an AP that is Arithmetic Progression. First installment is of Rs. 20, second is of Rs. 35, third is of Rs. 50, fourth is of Rs. 65 and so on and installments because loan gets cleared in n months and we also know that some of these n installments is equal to 3,250. Now sum of n terms of an AP is given by Sn and it is n by 2 into 2a plus n minus 1 into d. Now this is the first term of the AP, d is the common difference of the AP and n is the number of terms and we have to find the number of terms and here we know that the sum of these n terms is 3,250 so here Sn is 3,250, a the first term is 20, d the common difference is 15 as 35 minus 20 is 15, 50 minus 35 is 15 and so on. So now we put all these values in 1, so from 1 we have 3,250 is equal to n by 2 into 2a, a is 20 plus n minus 1 into d, d is 15 so we have 2 into 3,250 is 6,500 is equal to n into 40 plus 15n minus 15, minus 15, now again 6,500 is equal to n into 40 minus 15 is 25 plus 15n. So this implies 6,500 is equal to 25n plus 15n square. So this implies 15n square plus 25n minus 6,500 is equal to 0. Now taking 5 common from this equation we have 3n square plus 5n minus 1300 is equal to 0, now we will factorize this quadratic equation. So we have 3n square minus 65n plus 60n minus 1300 we should have plus 5n so it should be 65n minus 60n. So now taking n common from the first two terms we have n into 3n, n into 3n plus 65 and taking minus 20 common from the last two terms we have 3n plus 65 is equal to 0. Now taking 3n plus 65 common we have 3n plus 65 into n minus 20 is equal to 0. So this implies 3n plus 65 is equal to 0 or n minus 20 is equal to 0. So this implies 3n is equal to minus 65, n is equal to 20 and this implies n is equal to minus 65 upon 3 and from here we have n is equal to 20. Now since n is the number of months in which the loan gets cleared it cannot be minus 65 upon 3 so we reject this so we have n is equal to 20. So this completes the question and the session, bye for now take care have a good day.