## Monday, 31 October 2011

### 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
Solution:
Cost of scooter = Rs 22000
Initial payment at the time of purchase = Rs 4000
Balance unpaid amount = 22000-4000 = 18000
Annual installment after 1st year = (10% of 18000)+1000 = 1800+1000
Annual installment after 2nd year = (10% of 17000)+1000 = 1700+1000
etc.. etc.
Annual installment after 18th 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, Sn=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