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

\[\text { Let the cost price of the motorcycle for Ravish be Rs . x } . \]

\[\text { Loss % }= 28 % \]

\[\text { Therefore, SP = CP }\left( \frac{100 -\text {  Loss % }}{100} \right)\]

\[\text { SP = Rs . x }\left( \frac{72}{100} \right)\]

\[\text { Selling price of the motorcycle for Ravish = Cost price of the motorcycle for Vineet }\]

\[\text { Money spent on repairs = Rs } . 1680\]

\[\text { Therefore, total cost price of the motorcycle for Vineet = Rs } . ( x\left( \frac{72}{100} \right) + 1680)\]

\[\text { Selling price of the motorcycle for Vineet } = Rs . 35910\]

\[\text { Profit % = 12 . 5 % } \]

\[\text { SP = CP }\left( \frac{\text { Profit % } + 100}{100} \right)\]

\[ \Rightarrow 35910 = \left( \frac{72x}{100} + 1680 \right)\left( \frac{12 . 5 + 100}{100} \right)\]

\[ \Rightarrow 35910 \times 100 \times 100 = (72x + 168000)(112 . 5)\]

\[ \Rightarrow 359100000 = 8100x + 18900000\]

\[ \Rightarrow 340200000 = 8100x\]

\[ \Rightarrow x = Rs . 42000\]

\[\text { Therefore, Ravish bought the motorcycle for Rs }. 42000\]