A farmer buys a used tractor for Rs. 12000. H | vedclass

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Question

(A) The farmer pays $Rs. 6000$ in cash.Therefore,the unpaid amount is $Rs. 12000 - Rs. 6000 = Rs. 6000$.The farmer pays the balance in $12$ annual ins

Vedclass · Accepted Answer

$Rs. 16680$

Vedclass · Answer

(A) The farmer pays $Rs. 6000$ in cash.Therefore,the unpaid amount is $Rs. 12000 - Rs. 6000 = Rs. 6000$.The farmer pays the balance in $12$ annual instalments of $Rs. 500$ each,plus $12\%$ interest on the remaining unpaid amount.The unpaid amounts at the end of each year are $6000, 5500, 5000, \dots, 500$.The total interest paid is $12\%$ of $(6000 + 5500 + 5000 + \dots + 500)$.This is an Arithmetic Progression $(A.P.)$ where the first term $a = 500$,the last term $l = 6000$,and the number of terms $n = 12$.The sum of the $A.P.$ is $S_n = \frac{n}{2}(a + l) = \frac{12}{2}(500 + 6000) = 6(6500) = 39000$.Total interest $= 12\% 	ext{ of } 39000 = \frac{12}{100} 	imes 39000 = 12 	imes 390 = Rs. 4680$.Total cost of the tractor $= 	ext{Cash paid} + 	ext{Balance} + 	ext{Total interest} = 6000 + 6000 + 4680 = Rs. 16680$.

$A$ 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 will the tractor cost him?

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