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Question
A cycle merchant allows 20% discount on the marked price of the cycles and still makes a profit of 20%. If he gains Rs 360 over the sale of one cycle, find the marked price of the cycle.
Solution
\[\text { Given }, \]
\[\text { Gain on one cycle = Rs . } 360\]
\[\text { Gain = 20 % }\]
\[\text { Gain % } = \frac{\text { Gain }}{CP} \times 100\]
\[20 = \frac{360}{CP} \times 100\]
\[CP = Rs . 1800\]
\[SP = \frac{100 + \text { Gain % }}{100} \times CP\]
\[SP = \frac{120}{100} \times 1800 = Rs . 2160\]
\[\text { SP = Rs } . 2160\]
\[\text { Discount = 20 % } \]
\[\text { MP } = \frac{100 \times SP}{100 -\text { Discount % }}\]
\[\text { MP }= \frac{100 \times 2160}{80} = Rs . 2700\]
\[\text { Hence, the MP of one cycle is Rs } . 2700 .\]
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