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?

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 $16000 \ldots \ldots 10 \%$ of $1000$

Thus, total interest to be paid

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

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

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

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

Let the number of terms be $n$

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

$\Rightarrow n=18$

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

$=9[2000+17000]$

$=171000$

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

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

$\therefore$ cost of scooter $= Rs .22000+ Rs .17100= Rs .39100$