Question

Babubhai borrows Rs. $4000$ and agrees to repay with a total interest of Rs. $500$ in $10$ installment, each installment being less than the preceding installment by Rs. $10.$ What should be the first and the last installment?

• A. $495,405$
• B. $400,500$
  
• C. $365,315$
  
• D. $500,450$

Answer 1

The correct option is A $495,405$

Total money repaid by Babubhai in $10$ installments $=S_{10}=$ Principle $+$ interest

$\therefore s_{10}=4000+500=4500$

$\therefore$ number of installment $\left(n\right)=10$

$\because$ he repays each installment being less that the preceding installment by Rs. $10$

$\therefore$ difference between two consecutive installments $\left(d\right)=-10$

First installment $=a=?$

Last installment $\left(t_{10}\right)=?$

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

$\Rightarrow S_{10}=\frac{10}{2}[2a+(10-1)-10]$

$\Rightarrow 4500=5[2a+9(-10\left)\right]$

$\Rightarrow \frac{4500}{5}=2a-90$

$\Rightarrow 900=2a-90$

$\Rightarrow 2a=990$

$\Rightarrow a=495$ ........(1)

Now $t_n=a+(n-1)d$

$\Rightarrow t_n=495+(10-1)-10$

$\Rightarrow t_n=495+-90$

$\Rightarrow t_{10}=405$

$\therefore$ first installment $=495$

Last installment $=405$