Question

Ravish sold his motorcycle to Vineet at a loss of 28%. Vineet spent Rs 1680 on its repairs and sold the motor cycle to Rahul for Rs 35910, thereby making a profit of 12.5%, find the cost price of the motor cycle for Ravish.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{cost}\mathrm{price}\mathrm{of}the\mathrm{motorcycle}\mathrm{for}\mathrm{Ravis}hbe\mathrm{Rs}.\mathrm{x}. \\ \mathrm{Loss}\%=28\% \\ \mathrm{Therefore},\mathrm{SP}=\mathrm{CP}\left(\frac{100-\mathrm{Loss}\%}{100}\right) \\ \mathrm{SP}=\mathrm{Rs}.x\left(\frac{72}{100}\right) \\ \mathrm{Selling}\mathrm{price}\mathrm{of}\mathrm{the}\mathrm{motorcycle}\mathrm{for}\mathrm{Ravish}=\mathrm{Cost}\mathrm{price}\mathrm{of}\mathrm{the}\mathrm{motorcycle}\mathrm{for}\mathrm{Vineet} \\ \mathrm{Money}\mathrm{spent}\mathrm{on}\mathrm{repair}s=\mathrm{Rs}.1680 \\ Therefore,t\mathrm{otal}\mathrm{cost}\mathrm{price}\mathrm{of}\mathrm{the}\mathrm{motorcycle}\mathrm{for}\mathrm{Vineet}=\mathrm{Rs}.(x\left(\frac{72}{100}\right)+1680) \\ \mathrm{Selling}\mathrm{price}\mathrm{of}\mathrm{the}\mathrm{motorcycle}\mathrm{for}\mathrm{Vineet}=\mathrm{Rs}.35910 \\ \mathrm{Profit}\%=12.5\% \\ \mathrm{SP}=\mathrm{CP}\left(\frac{\mathrm{Profit}\%+100}{100}\right) \\ \Rightarrow 35910=\left(\frac{72x}{100}+1680\right)\left(\frac{12.5+100}{100}\right) \\ \Rightarrow 35910\times 100\times 100=(72x+168000)(112.5) \\ \Rightarrow 359100000=8100x+18900000 \\ \Rightarrow 340200000=8100x \\ \Rightarrow x=\mathrm{Rs}.42000 \\ \mathrm{Therefore},\mathrm{Ravis}hboughtthemotorcyclefor\mathrm{Rs}.42000 \end{gathered}$$