Q.4 (iii) Ajay Sharma repays the borrowed amount of ₹ 3,25,000 by paying ₹ 30,500 in the first month and then decreases the payment by ₹ 1,500 every month. How long will it take to clear his amount ?
Best answer
Answer: 20 months
The monthly payments form an A.P. with \(a = 30500\), \(d = -1500\) and \(S_n = 3{,}25{,}000\).
\(S_n = \dfrac{n}{2}[2a + (n-1)d]\)
\(325000 = \dfrac{n}{2}[2(30500) + (n-1)(-1500)] = \dfrac{n}{2}[61000 - 1500n + 1500]\)
\(650000 = n(62500 - 1500n)\)
\(1500n^2 - 62500n + 650000 = 0\)
Dividing by 500: \(3n^2 - 125n + 1300 = 0\).
\(n = \dfrac{125 \pm \sqrt{15625 - 15600}}{6} = \dfrac{125 \pm 5}{6}\)
\(n = \dfrac{130}{6}\) (not a natural number) or \(n = \dfrac{120}{6} = 20\).
So it will take 20 months to clear the amount. (Check: \(S_{20} = 10[61000 - 28500] = 3{,}25{,}000\) ✓)
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