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Ramakanth repays a loan of rs. 6500 by paying rs. 40 in the first month and then increasing the payment by rs. 30 every month. In how many months will he be able to clear the loan? Hint: Sn=n/2[2a+(n-1)d] |
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Answer» Answer: 20 months Step-by-step explanation: Given A MAN repays a loan of rs 6500 by paying rs 40 in the first month and then INCREASING the payment by rs 30 every month. How long will it take for him to clear the loan? Let the loan be cleared in n months. Now the amount is in A.P . Let the first payment be 40 So second will be 40+ 30 Third will be 40 + 30+ 30and so on. So S = 40 + 70+ 100+….and so on. a = 40 d = 30 Now sum to n terms is given by Sn = [n/2 (2 a + (n – 1) d] 65,00 = [n/2 (80+ (n – 1)30] 1,30,00 = 50 n + 30 n^2 30 n^2 + 50 n – 1,30,0=0 Divide through by 50: 3n² + 5n - 130= 0 Now solve for n. The roots are - 60 and 65 We EXPAND the equation below : 3n²- 60n + 65n - 1300= 0 3n(n - 20) + 65(n - 20) = 0 (3n + 65)(n - 20) = 0 3n = - 65 n = - 65/3 n = 20 n = - 65/3 or 20 Since n is an integer and a positive number, we will take 20. |
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