Question

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 mcuh will the scooter cost him ?

Answer 1

Total cost of scooter = Rs. 22000

Cash amount paid = Rs. 4000

Balance amount = 22000 - 4000 = Rs. 18000

Interest of first instalment

$=\frac{18000\times 10\times 1}{100}=Rs.1800$

Amount of first instalment

= 1000 + 1800 = Rs. 2800

Interest of second instalment

$=\frac{17000\times 10\times 1}{100}=Rs.1700$

Amount of second instalment

= 1000 + 1700 = Rs. 2700

Interest of third instalment

$=\frac{16000\times 10\times 1}{100}=Rs.1600$

Amount of third instalment

= 1000 + 1600 = Rs. 2600

The sequence of instalments is 2800, 2700, 2600 ...

Here a = 2800, d = 2700 - 2800 = -100 and n = 18

$\therefore S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$\therefore S_n=\frac{18}{2}[2\times 2800+(18-1)\times -100]$

= 9[5600 - 1700] = Rs. 35100

Thus total cost of scooter

= 35100 + 4000 = Rs. 39100.