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?
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 $= Rs .22000+ Rs .17100= Rs .39100$
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