Question

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

Answer 1

Total money repaid by Babubhai in $1010$ Interest

∴ $S10=4000+500$

∴$S10=Rs.4500$

∵ He repays each instalment being less than the preceding instalment by Rs. $1010$

∴ Difference between two consecutive installments $d=-10$

We know that,

$Sn=n2[2a+(n–1\left)d\right]$

∴ $S10=102[2a+(10–1\left)d\right]$

∴ $4500=5[2a+9(–10\left)\right]$

∴ $900=2a–90$

∴ $900+90=2a$

∴ $990=2a$

∴ $a=495$

Now, $tn=a+(n–1)dtn=a+(n–1)d$

∴ $t10=a+(10–1)dt10=a+(10–1)d$

∴ $t_{10}=495+9(–10)$

∴ $10=495–90$

∴ $t10=405$