Question

A farmer borrows Rs. $1,000$ and agrees to repay with a total interest of Rs. $140$ in $12$ installments, each installment being less than the preceding installment by Rs $10$. What should be his first installment?

Answer 1

Repay with a total $12$ instalment $=$ Rs. $140$
$\therefore$ Total of $12$ instalment $S_{12}=$ Rs $(1,000+140)$
$=$ Rs. $1140$
Number of instalments $\left(n\right)=12$
Let first instalments $=a$
Difference $\left(d\right)=-10$
$\therefore S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
$\therefore S_{12}=\frac{12}{2}[2a+11\times (-10\left)\right]$
$\Rightarrow 1140=6[2a-110]$
$\Rightarrow 2a-110=190$
$\Rightarrow 2a=300$
$a=150$
$\therefore$ First instalment is Rs. $150$.