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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.
Solution
\[\text { Let the cost price of the motorcycle for Ravish be Rs . x } . \]
\[\text { Loss % }= 28 % \]
\[\text { Therefore, SP = CP }\left( \frac{100 -\text { Loss % }}{100} \right)\]
\[\text { SP = Rs . x }\left( \frac{72}{100} \right)\]
\[\text { Selling price of the motorcycle for Ravish = Cost price of the motorcycle for Vineet }\]
\[\text { Money spent on repairs = Rs } . 1680\]
\[\text { Therefore, total cost price of the motorcycle for Vineet = Rs } . ( x\left( \frac{72}{100} \right) + 1680)\]
\[\text { Selling price of the motorcycle for Vineet } = Rs . 35910\]
\[\text { Profit % = 12 . 5 % } \]
\[\text { SP = CP }\left( \frac{\text { Profit % } + 100}{100} \right)\]
\[ \Rightarrow 35910 = \left( \frac{72x}{100} + 1680 \right)\left( \frac{12 . 5 + 100}{100} \right)\]
\[ \Rightarrow 35910 \times 100 \times 100 = (72x + 168000)(112 . 5)\]
\[ \Rightarrow 359100000 = 8100x + 18900000\]
\[ \Rightarrow 340200000 = 8100x\]
\[ \Rightarrow x = Rs . 42000\]
\[\text { Therefore, Ravish bought the motorcycle for Rs }. 42000\]
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