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Question
A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much the tractor cost him?
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Solution
Cost of the tractor = Rs 12000
It is given that the farmer pays Rs 6000 in cash.
Unpaid amount = Rs 6000
He has to pay Rs 6000 in annual instalments of Rs 500 plus 12% interest on the unpaid amount.
∴ Number of years taken by the farmer to pay the whole amount = 6000
\[\div\] 500 = 12
Hence, the interest paid by farmer annually would be as follows:
12 % of Rs 6000 + 12 % of Rs 5500 + 12 % of Rs 5000
\[ = 720 + 660 + 600 . . . . \]
It is in an A.P. where a = 720 , d = \[-\] 60 \text { and } n = 12.
Total sum:
\[\frac{12}{2}\left[ 2 \times 720 + 11 \times - 60 \right]\]
\[ = 6\left[ 1440 - 660 \right]\]
\[ = \text {Rs }4680\]
∴ Amount the farmer has to pay = Rs 12000 + Rs 4680 = Rs 16680
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