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 will the tractor cost him?

Answer 1

It is given that the farmer pays Rs 6000 in cash.
Therefore, unpaid amount = Rs 12000 -Rs 6000
= Rs 6000 According to the given condition, the interest paid annually is 12% of 6000, 12% of 5500, 12% of 5000, …, 12% of 500
Thus, total interest to be paid = 12% of 6000 + 12% of 5500 + 12% of 5000 + … + 12% of 500
= 12% of (6000 + 5500 + 5000 + … + 500)
= 12% of (500 + 1000 + 1500 + … + 6000)
Now, the series 500, 1000, 1500 … 6000 is an A.P. with both the first term and common difference equal to 500.
Let the number of terms of the A.P. be n.
∴ 6000 = 500 + (n -1) 500
⇒ 1 + (n -1) = 12
⇒ n = 12
∴Sum of the A.P = \(=\frac{12}{2}[2 (500) + (12 - 1) (500)] = 6 [1000 + 5500] = 6 (6500) = 39000\)
Thus, total interest to be paid = 12% of (500 + 1000 + 1500 + … + 6000)
= 12% of 39000 = Rs 4680
Thus, cost of tractor = (Rs 12000 + Rs 4680) = Rs 16680.