Q. 284.1( 30 Votes )

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 :

Amount Paid to buy scooter = Rs. 22,000


Shamshad Pays Cash = Rs. 4000


Remaining Balance = Rs. (22000 - 4000) = 18000


Annual Instalment = Rs 1000 + [email protected]% on unpaid amount


1st Instalment


Unpaid Amount = Rs. 18000


Interest on Unpaid Amount = (10/100) × 18000 = 1800


Amount of Instalment = Rs. 1000 + Rs. 1800 = Rs. 2800


2nd Instalment


Unpaid Amount = Rs. (18000 - 1000) = Rs. 17000


Interest on Unpaid Amount = (10/100) × 17000 = 1700


Amount of Instalment = Rs. 1000 + Rs. 1700 = Rs. 2700


3rd Instalment


Unpaid Amount = Rs. (17000 - 1000) = Rs. 16000


Interest on Unpaid Amount = (10/100) × 16000 = 1600


Amount of Instalment = Rs. 1000 + Rs. 1600 = Rs. 2600


Total no. of Instalments = 18000/1000 = 18


Thus, Annual Instalments are 2800, 2700, 2600, …upto 18 terms


Since the common difference between the consecutive terms is constant. Thus, Annual Instalments are in AP.


Here


first term(a) = 2800


Common difference(d) = 2700 - 2800 = - 100


Number of terms(n) = 18


Total amount paid in 12 instalments is given by -


Sn = (n/2)[2a + (n - 1)d]


S18 = (18/2)[2(2800) + (18 - 1)( - 100)]


= 9[5600 + 17( - 100)]


= 9[5600 - 1700]


= 9 × 3900


= 35100


Hence, total amount paid in 12 Instalments = Rs 35100


Hence,


Total Cost of Tractor


= Amount paid earlier + Amount paid in 12 Instalments


= Rs. (4000 + 35100)


= Rs. 39100


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