Question

Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?

Answer 1

It is given that Shamshad Ali buys a scooter for Rs 22000 and pays Rs 4000 in cash.
∴Unpaid amount = Rs 22000 - Rs 4000 = Rs 18000
According to the given condition, the interest paid annually is 10% of 18000, 10% of 17000, 10% of 16000 … 10% of 1000
Thus, total interest to be paid = 10% of 18000 + 10% of 17000 + 10% of 16000 + … + 10% of 1000
= 10% of (18000 + 17000 + 16000 + … + 1000)
= 10% of (1000 + 2000 + 3000 + … + 18000)
Here, 1000, 2000, 3000 … 18000 forms an A.P. with first term and common difference both equal to 1000. Let the number of terms be n.
∴ 18000 = 1000 + (n - 1) (1000)
⇒ n = 18
∴ 1000 + 2000 + ..... + 18000 = \(\frac{18 }{ 2} [2 (1000) + (18 - 1)(1000)]\)
                                                \(  =9 [2000 + 17000]\)
                                                 \(= 171000\)
∴ Total interest paid = 10% of (18000 + 17000 + 16000 + … + 1000)
= 10% of Rs 171000 = Rs 17100
∴Cost of scooter = Rs 22000 + Rs 17100 = Rs 39100.