A farmer buys a used for ₹180000. He pays ₹90000 in cash and agrees to pay the balance in annual instalments of ₹9000 plus 12% interest on the unpaid amount. How much did the tractor cost him?
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Given: -
The amount that is to be paid to buy a tractor = ₹180000.
An amount that he paid by cash = ₹90000.
Remaining balance = ₹90000
Annual instalment = ₹9000 + interest @12% on unpaid amount.
UNPAID AMOUNT | Interest on the unpaid amount | Amount of the instalment | |
1st instalment | 90000 | = | = 9000 + 10800 = 19800 |
2nd instalment | 81000 | = 9000 + 9720 = 18720 |
Thus, our instalments are 19800, 18720, 17640…….
Total number of instalments =
=
= 10
So our instalments are 19800, 18720, 17640 ... upto 10 terms.
All our instalments are in A.P with a common difference d.
Here
First term(a) = 19800
Common difference = d = 18720 - 19800
d = - 1080
Number of terms is 10
Sum of all instalments
= 149400
Hence,
The total cost of the scooter = amount that is paid earlier + amount paid in 10 instalments.
= 90000 + 149400
∴The total cost paid by the farmer = ₹239400