Progressions-4 (NCERT)

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 (in Rupees)?

 (1) 18000 * (1.1)¹⁷   (2) 18000 * (1.1)¹⁸   (3) 39100   (4) 37300   (5) None of these

Answer follows here:

Solution:

Cost of scooter = Rs 22000

Initial payment at the time of purchase = Rs 4000

Balance unpaid amount = 22000-4000 = 18000

Annual installment after 1^st year = (10% of 18000)+1000 = 1800+1000

Annual installment after 2^nd year = (10% of 17000)+1000 = 1700+1000

                            etc.. etc.

Annual installment after 18^th year = (10% of 1000)+1000 = 1000+1000

Hence, amount paid from all installments = (1800+1700+…..+1000) + 18(1000)

Observe that interest part is in a series of A.P.

Applying formula for sum to n terms of AP, S_n=n/2 (2a+(n-1)d), where a = initial term =1800; n = number of terms=18 and d = common difference =-100

Amount paid from all installments = 18/2 (2*1800 + (18-1)*(-100)) + 18000

                                                                = 9(3600-1700) + 18000 = 35100

Total amount paid   = Initial payment + amount paid from all installments

                                    = 4000+35100 = 39100

Answer (3)