Imrez buys a used car for 150000 he pays 100000 cash and agress to pay the balance in annual instalments of 5000 plus 8% interest on the unpaid amount . How much will the car cost for him.

Dear Student,

Please find below the solution to the asked query:
$$\begin{gathered} \mathrm{Total} \mathrm{cost}=150000 \mathrm{Rs} \\ \mathrm{Unpaid}=150000-100000=50000 \mathrm{Rs} \\ \mathrm{According} \mathrm{to} \mathrm{the} \mathrm{problem} , \mathrm{the} \mathrm{interest} \mathrm{paid} \mathrm{annually} \mathrm{is} \\ 8\% \mathrm{of} 50000+8\% \mathrm{of} 45000+8\% \mathrm{of} 40000+...+8\% \mathrm{of} 5000 \\ \Rightarrow 8\% \mathrm{of} \left(5000+10000+15000+20000+....+50000\right) \\ \left(5000+10000+15000+20000+....+50000\right) \mathrm{are} \mathrm{in} \mathrm{AP} \\ \mathrm{So} \\ 50000=5000+\left(\mathrm{n}-1\right)5000 \\ 10=\mathrm{n} \\ \mathrm{So} \\ 50000=\frac{10}{2}\left[2\left(5000\right)+\left(10-1\right)5000\right]=5\left(10000+45000\right)=5\left(55000\right)=275000 \\ \mathrm{So} \\ \mathrm{Total} \mathrm{interest} \mathrm{paid}=8\% \mathrm{of} 275000=275000\times \frac{8}{100}=2750\times 8=22000 \\ \mathrm{So} \mathrm{cost} \mathrm{of} \mathrm{car}=150000+22000=\mathrm{Rs}172000 \mathrm{Answer} \end{gathered}$$

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