Arun buys a scooter for ₹44000. He pays ₹8000 in cash and agrees to pay the balance in annual instalments of ₹4000 each plus 10% interest on the unpaid amount. How much did he pay for it?
Given:
The amount that is to be paid to buy a scooter = 44000
The amount that he paid by cash = ₹8000
Remaining balance = ₹36000
Annual instalment = ₹4000 + interest@10% on the unpaid amount
Thus, our instalments are 7600, 7200, 6800…….
Total number of instalments $=\frac{\text { The remaining balance left }}{\text { balance that is cleared per instalment }}$
$=\frac{36000}{4000}$
= 9
So our instalments are 7600, 7200, 6800 ... up to 9 terms.
Hint: - All our instalments are in A.P with a common difference of 400.
Here
First term, a = 7200
Common difference = d = 7200 - 7600
d = - 400
Number of terms = 9
Sum of all instalments $=s_{n}=\frac{n}{2}\{2 \times a+(n-1) \times d\}$
$=\frac{9}{2}\{2 \times 7600+(9-1) \times(-400)\}$
= 54000
Hence,
The total cost of the scooter = amount that is paid earlier + amount paid in 9 instalments.
= 8000 + 54000
= 62000
∴The total cost paid by Arun = 62000