Question:

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?

Solution:

It is given that Shamshad Ali buys a scooter for Rs 22000 and pays Rs 4000 in cash.

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

According to the given condition, the interest paid annually is

$10 \%$ of $18000,10 \%$ of $17000,10 \%$ of $16000 \ldots 10 \%$ of 1000

Thus, total interest to be paid $=10 \%$ of $18000+10 \%$ of $17000+10 \%$ of $16000+\ldots+10 \%$ of 1000

$=10 \%$ of $(18000+17000+16000+\ldots+1000)$

$=10 \%$ of $(1000+2000+3000+\ldots+18000)$

Here, 1000, 2000, 3000 … 18000 forms an A.P. with first term and common difference both equal to 1000.

Let the number of terms be n.

$\therefore 18000=1000+(n-1)(1000)$

$\Rightarrow n=18$

$\therefore 1000+2000+\ldots . .+18000=\frac{18}{2}[2(1000)+(18-1)(1000)]$

$=9[2000+17000]$

$=171000$

$\therefore$ Total interest paid $=10 \%$ of $(18000+17000+16000+\ldots+1000)$

$=10 \%$ of Rs $171000=$ Rs 17100

$\therefore$ Cost of scooter $=$ Rs $22000+$ Rs $17100=$ Rs 39100