# Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalments of Rs 1000 plus 10% interest on the unpaid amount.

Question:

Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalments of Rs 1000 plus 10% interest on the unpaid amount. How much the scooter will cost him.

Solution:

Cost of the scooter = Rs 22000

Shamshad Ali pays Rs 4000 in cash.

$\therefore$ Unpaid amount $=$ Rs $22000-$ Rs $4000=$ Rs 18000

Number of years taken by Shamshed Ali to pay the whole amount $=18000 \div 1000=18$

He agrees to pay the balance in annual instalments of Rs 1000 plus 10% interest on the unpaid amount.

Total amount of instalments:

$10 \%$ of Rs $18000+10 \%$ of Rs $17000+10 \%$ of Rs $16000 \ldots$

$=1800+1700+1600 \ldots$

It is in an A.P. where $a=1800, d=-100$ and $n=18$.

Therefore, total amount of instalments:

$\frac{18}{2}[2 \times 1800+(18-1) \times-100]$

$=9[3600-1700]$

$=\operatorname{Rs} 17100$

∴ Total amount Shamshad Ali has to pay = Rs (22000 + 17100) = Rs 39100