Question

Ramesh wants to buy a cell phone. He can buy it by paying Rs. $15,000$ cash or by making $12$ monthly instalments as $Rs.1800$ in the 1st month, Rs. $1750$ in $2$nd month $Rs.1700$ in $3rd$ month and so on. If he pays the money in instalments. find
(i) total amount paid in $12$ instalments
(ii) how much extra he has to pay over and above the cost price.

Answer 1

Here, arithmetic series is,
1800 + 1750 + 1700 + .........
$a=1800,d=T_2-T_1=1750-1800=-50,n=12,S_{12}=?$
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
$S_{12}=\frac{12}{2}\left[2\right(1800)+(12-1\left)\right(-50\left)\right]$
$S_{12}=6[3600+11(-50\left)\right]=6[3600-550]$
$S_{12}=6\times 3050=18,300$
$\therefore$ Total amount paid in 12 instalments $=Rs.18,300$
Extra amount paid $=Rs.18,300-Rs.15,000=Rs.3,300.$