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Previous Year Question (PYQs)

A man repays a loan of ₹ $3250$ by paying ₹ $20$ in the first month and then increases the payment by ₹ $15$ every month. How long will it take him to clear the loan?




Solution

Here, $a=20,\ d=15$ $ S_n=\frac{n}{2}[2a+(n-1)d] $ $ 3250=\frac{n}{2}[40+(n-1)15] $ $ \Rightarrow 3250=\frac{n}{2}(40+15n-15) $ $ \Rightarrow 3250=\frac{n}{2}(15n+25) $ $ \Rightarrow n(15n+25)=6500 $ $ \Rightarrow 3n^2+5n-1300=0 $ $ \Rightarrow (3n+65)(n-20)=0 $ $ \Rightarrow n=20 $

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