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

Given: Shamshad Ali buys a scooter for Rs 22,000 and pays Rs 4,000 in cash.

∴ Unpaid amount = Rs 22,000 − Rs 4,000 = Rs 18,000

According to the given condition, the interest paid annually is:

10% of 18,000, 10% of 17,000, 10% of 16,000, …, 10% of 1,000

Thus, total interest to be paid = 10% of (18,000 + 17,000 + 16,000 + … + 1,000)

= 10% of (1,000 + 2,000 + 3,000 + … + 18,000)

Here, 1,000, 2,000, 3,000, …, 18,000 form an A.P. with first term a = 1,000 and common difference d = 1,000.

Let the number of terms be n.

18,000 = 1,000 + (n − 1)×1,000 ⇒ n = 18

∴ Sum of A.P. = (n/2)[2a + (n − 1)d]

= (18/2)[2(1,000) + (18 − 1)(1,000)]

= 9[2,000 + 17,000] = 9×19,000 = 171,000

∴ Total interest paid = 10% of Rs 171,000 = Rs 17,100

∴ Cost of scooter = Rs 22,000 + Rs 17,100 = Rs 39,100

Hence, the total cost of the scooter is Rs 39,100.