Question

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

Answer 1

Given Shamshad Ali buys a scooter for Rs. 22000 and pay Rs4000 in cash $\Rightarrow$ Unpaid amount $=22000-4000=Rs18000$.

At the end of first year , interest paid $=10$% of 18000

Amount paid as instalment at the end of 1 year =Rs1000.

So, loan amount left $=Rs18000-1000=Rs17000$

Now, at the end of second year , interest paid $10$% of 17000

Amount paid as instalment at the end of second year = Rs1000

So, loan amount left $=Rs17000-1000=Rs16000$

So, total interest to be paid =10% of 18000+10% of 17000+10% of 16000+...+10% of 1000.
$=10$% of $(18000+17000+16000+...1000)$
$=10$% of $(1000+2000+3000+...+18000)$ ....(1)
Here, 1000, 2000, 3000, ...18000 forms an A.P. with both the first term and common difference equals to 1000.
Let the number of terms of A.P.be n.
$\therefore 18000=1000+(n-1)\left(1000\right)$

$\Rightarrow n=18$

$\therefore S_{18}=1000+2000+...+18000$

$=\frac{18}{2}\left[2\right(1000)+(18-1\left)\right(1000\left)\right]$

$=9[2000+17000]=171000$

So, by eqn(1),

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

$=10$% of $Rs.1,71,000$

$=Rs.17,100$

So, the cost of scooter to him is $Rs.22000+17100=39100$