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Last updated at May 29, 2018 by Teachoo
Misc 27 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 be the tractor cost him? Amount paid to buy tractor = Rs 12,000 He pays cash = Rs 6000 Remaining balance = 12000 β 6000 = 6000 Annual instalment = Rs 500 + interest@12% on unpaid amount Thus, our instalments are 1220, 1160, 1100,β¦. Total number of instalments = (π ππππππππ πππππππ ππππ‘)/(π΅ππππππ πππππππ πππ πππ π‘ππππππ‘) = 6000/500 = 12 Thus, our instalments are 1220, 1160 , 1100 , β¦ upto 12 terms We can observe that this is an AP as difference between consecutive terms is an AP Here first term (a) = 1220 common difference = d = 1160 β 1220 = β 60 number of terms = n = 12 We need to calculate total amount paid in 12 instalments i.e. (1220 + 1160 + 1100 + β¦ upto 12 terms) We use the formula, Sn = π/2 (2a + (n β 1)d) Where, Sn = sum of n terms of A.P. n = number of terms a = first term and d = common difference Putting value of n = 12 , a = 1220 & d = β60 S12 = 12/2 [ 2(1220)+(12 β 1) (β 60) ] = 6[ 2440 + (β 60)11] = 6[ 2440 β 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) = 16680