Question

Shamshad Ali buys a scooter for $\text{Rs}22000$. He pays $\text{Rs}4000$ cash and agrees to pay the balance in annual instalment of $\text{Rs}1000$ plus $10\%$ interest on the unpaid amount. How much will the scooter cost him$?$

Answer 1

Step $1$.Solving given data .

Given, Shamshad Ali buys a scooter for $\text{Rs}22000$ and pays $\text{Rs}4000$ in cash.
So, the unpaid amount $=\text{Rs}22000-\text{Rs}4000=\text{Rs}18000$

According to the question, the annually paid interest is
$10\%\text{of}18000,10\%\text{of}17000,10\%\text{of}16000,.....,10\%\text{of}1000$

Hence, the total interest to be paid $=10\%\text{of}18000+10\%\text{of}17000+10\%\text{of}16000+\dots +10\%\text{of}1000$
$=10\%\text{of}(18000+17000+16000+\dots +1000)$
$=10\%\text{of}(1000+2000+3000+\dots +18000)\dots \left(1\right)$

Step $2$. Finding number of instalments.

The series $1000,2000,3000\dots 18000$ forms an A.P. with first term $a=1000$ and common difference $d=1000$.
Let's take the number of terms to be $n$

So,
$18000=1000+(n-1)\left(1000\right)$
$n=\frac{18000}{1000}$
$n=18$

Step $3$. Finding total cost of scooter.

Now $a=1000,d=1000andn=18$

Now, the sum of the A.P is given by:
$\therefore 1000+2000+\dots .+18000=\frac{18}{2}\left[2\right(1000)+(18-1\left)\right(1000\left)\right]$
$=9[2000+17000]$
$=9\times 19000$
$=171000$
So, total interest to be paid $=10\%\text{of}(1000+2000+3000+\dots +18000)$ {from $\left(1\right)$}

$=10\%of\text{Rs}171000=\text{Rs}17100$ Therefore, the cost of scooter $=\text{Rs}22000+\text{Rs}17100=\text{Rs}39100$