Question

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

Answer 1

Babu bhai borrows Rs 4000.
Total interest he has to pay = Rs 500
Now,

$$\begin{gathered} \mathrm{Rs}4500\mathrm{is}\mathrm{the}\mathrm{total}\mathrm{sum}\mathrm{of}\mathrm{money}\mathrm{he}\mathrm{has}\mathrm{to}\mathrm{repay}. \\ \mathrm{Each}\mathrm{instalment}\mathrm{is}\mathrm{less}\mathrm{than}\mathrm{the}\mathrm{preceding}\mathrm{instalment}\mathrm{by}\mathrm{Rs}10. \\ \mathrm{We}\mathrm{know}: \\ {S}_n=\frac{n}{2}\left[2a+(n-1)d\right] \\ \Rightarrow 4500=\frac{n}{2}\left[2a+(n-1)d\right](n=10\mathrm{and}d=-10) \\ \Rightarrow 4500=\frac{10}{2}\left[2a+9\times -10\right] \\ \Rightarrow 900=2a-90 \\ \Rightarrow 990=2a \\ \Rightarrow a=\frac{990}{2}=495 \\ \mathrm{Therefore},\mathrm{the}\mathrm{first}\mathrm{term}\mathrm{is}495. \\ \mathrm{Now},\mathrm{we}\mathrm{have}\mathrm{to}\mathrm{find}\mathrm{the}\mathrm{last}\mathrm{term},\mathrm{i}.\mathrm{e}.,\mathrm{the}{10}^{\mathrm{th}}\mathrm{term}. \\ \mathrm{We}\mathrm{know}: \\ {t}_n=a+(n-1)d \\ =495+(10-1)\times \left(-10\right) \\ =495-90 \\ =405 \\ \mathrm{Therefore},\mathrm{the}\mathrm{last}\mathrm{term}\mathrm{is}405. \end{gathered}$$

Thus, the first and last instalments are Rs 495 and Rs 405, respectively.