Q. 274.3( 39 Votes )

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?

Answer :

Amount Paid to buy tractor = Rs. 12,000


Farmer Pays Cash = Rs. 6000


Remaining Balance = 12000 - 6000 = 6000


Annual Instalment = Rs 500 + [email protected]% on unpaid amount


1st Instalment


Unpaid Amount = Rs. 6000


Interest on Unpaid Amount = (12/100) × 6000 = 720


Amount of Instalment = Rs. 500 + Rs. 720 = Rs. 1220


2nd Instalment


Unpaid Amount = Rs. (6000 - 500) = Rs. 5500


Interest on Unpaid Amount = (12/100) × 5500 = 6600


Amount of Instalment = Rs. 500 + Rs. 660 = Rs. 1160


3rd Instalment


Unpaid Amount = Rs. (5500 - 500) = Rs. 5000


Interest on Unpaid Amount = (12/100) × 5000 = 600


Amount of Instalment = Rs. 500 + Rs. 600 = Rs. 1100


Total no. of Instalments = 6000/500 = 12


Thus, Annual Instalments are 1220, 1160, 1100, …upto 12 terms


Since the common difference between the consecutive terms is constant. Thus, Annual Instalments are in AP.


Here


first term(a) = 1220


Common difference(d) = 1160 - 1220 = - 60


Number of terms(n) = 12


Total amount paid in 12 instalments is given by -


Sn = (n/2)[2a + (n - 1)d]


S12 = (12/2)[2(1220) + (12 - 1)( - 60)]


= 6[2440 + 11( - 60)]


= 6[2440 - 660]


= 6 × 1780


= 10680


Hence, total amount paid in 12 Instalments = Rs 10680


Hence,


Total Cost of Tractor


= Amount paid earlier + Amount paid in 12 Instalments


= Rs. (6000 + 10680)


= Rs. 16680


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