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Question:
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Shamshad Ali buys a scooter for $₹ 22000$. he pays $₹ 4000$ cash and agrees to pay the balance in annual instalment of $₹ 1000$ plus $10 \%$ interest on the unpaid amount. How much will the scooter cost him ?
Solution:
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Verified Answer
Total cost of a scooter $=₹ 22000$
Paid cash $=₹ 4000$
Balance $=$ ₹ 18000
Number of instalments@ ₹1000 each =18
Interest on first instalment $=₹ \frac{18000 \times 10 \times 1}{100}$
=₹ 1800
$\therefore$ First instalment $=₹ 1000+1800=₹ 2800$
Interest on second instalment
$=₹ \frac{17000 \times 10 \times 1}{100}=₹ 1700$
$\therefore$ Second instalment $=₹ 1000+1700$
$=₹ 2700$
Interest on third instalment
$=₹\left(\frac{16000 \times 10 \times 1}{100}\right)=₹ 1600$
Third instalment $=₹(1000+1600)=₹ 2600$
$\therefore$ Total amount paid in instalments
$=₹(2800+2700+2600+\ldots \ldots \ldots \ldots+18$ terms $)$
$a=2800, d=-100, n=18$
$\begin{aligned}
S=& \frac{18}{2}[2 \times 2800+(18-1)(-100)] \\
&=9(5600-1700)=9 \times 3900=35100
\end{aligned}$
Scooter with cost him $₹(4000+35100)$ $=₹ 39100$
Paid cash $=₹ 4000$
Balance $=$ ₹ 18000
Number of instalments@ ₹1000 each =18
Interest on first instalment $=₹ \frac{18000 \times 10 \times 1}{100}$
=₹ 1800
$\therefore$ First instalment $=₹ 1000+1800=₹ 2800$
Interest on second instalment
$=₹ \frac{17000 \times 10 \times 1}{100}=₹ 1700$
$\therefore$ Second instalment $=₹ 1000+1700$
$=₹ 2700$
Interest on third instalment
$=₹\left(\frac{16000 \times 10 \times 1}{100}\right)=₹ 1600$
Third instalment $=₹(1000+1600)=₹ 2600$
$\therefore$ Total amount paid in instalments
$=₹(2800+2700+2600+\ldots \ldots \ldots \ldots+18$ terms $)$
$a=2800, d=-100, n=18$
$\begin{aligned}
S=& \frac{18}{2}[2 \times 2800+(18-1)(-100)] \\
&=9(5600-1700)=9 \times 3900=35100
\end{aligned}$
Scooter with cost him $₹(4000+35100)$ $=₹ 39100$
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