 Hello and welcome to the session. Let us discuss the following question. It says a household article is available for rupees 2,500 cash or rupees 520 cash down payment followed by four equal monthly installments. If the rate of interest charged under the installment plan is 25% per annum, find the amount of each installment. So we have to find the amount of each installment. If the rate of interest charged is 25% per annum. So let us now move on to the solution. First of all, we write the cash price or CP of the household article and it is given to be rupees 2,500 and we are given that the cash down payment is rupees 520. Now if the cash down payment is rupees 520 then the balance due will be that is the amount left after paying rupees 520 will be rupees 2,500 minus 520 and that is equal to rupees 1,980. Now we are given that the rate of interest 25%. Now we have to pay the balance due in four equal monthly installment. So the number of installments is 4. Now let amount of each installment be equal to rupees x. So now the amount paid in the installment scheme that is amount paid in four installments is rupees 4x because number of installments are 4 and amount of each installment is rupees x. So the amount paid in four installments is rupees 4x. Now the sixth step is the interest paid in installment scheme is rupees the total amount paid minus the balance due right. So now the principle for the first month equal to rupees 1,980 because balance due after paying rupees 520 is rupees 1,920. The principle for second month is rupees 1,980 minus x because amount of each installment is rupees x and the principle for the first month is 1,980. So principle for the second month is 1,980 minus rupees x because we have paid rupees x as the first installment. So principle left for the second month is this. Similarly, principle for third month is rupees 1,980 minus x that is the principle for the second month minus the amount of the second installment that is it is 1,980 minus 2x. Similarly, principle for the fourth month is rupees principle for the third month minus this installment paid in the third month. So this is equal to rupees 1,980 minus 3x. Now the total principle for one month will be the sum of all the principles. So it is 1,980 plus 1,980 this plus this plus this plus this it is 7,920 minus minus 2x minus 3x is minus 6x. So this was the seventh step interest given by principle into rate of interest into time upon 100. Now we have interest rupees 4x minus 1,980 as we obtained in step principle for one month or the total principle is rupees 7,920 minus 6x and the rate of interest as we know that it is 25 percent. So the interest principle that is 7,920 minus 6x into R that is 25 into T. Now T is 1 by 12 since we have obtained the principle for one month. So we will take the time as one month not as per annum. So we have time as 1 by 12 upon 100. So this is equal to now the interest is 4x minus 1,980 is equal to 7,920 minus 6x into 25 into 1 upon 100 into 12. Now 25 into 4 is 100. So again we have 4x minus 1,980 is equal to 7,920 minus 6x upon 4 into 12 that is 48. Now cross multiplying 48 into 4x minus 1,980 is equal to 7,920 minus 6x. So this implies 48 into 4x is 1,98 it's 1,92x minus 1,980 into 48 is 95040 and this is equal to 7,920 minus 6x. So this implies 1,92x plus 6x is equal to 7,920 plus 95040. So this implies 198x is equal to 102,960 adding the two. So this implies x is equal to 102,960 upon 198. So cancelling 102,960 by 198 that gives us x as 520. Therefore amount of each installment. So this completes the question and the session by for now take care. Have a good day.