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Question
After allowing a discount of 20% on the marked price of a lamp, a trader loses 10%. By what percentage is the marked price above the cost price?
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Solution
\[\text { Let the CP of the lamp be Rs } . 100 . \]
\[\text { Loss = 10 % of CP = Rs } . 10\]
\[\text { So, SP = CP - Loss = Rs . 100 - Rs . 10 = Rs } . 90\]
\[\text { The trader allows a discount of 20 % } . \]
\[\text { This means that when the MP is Rs . 100, the SP will be Rs } . 80 . \]
\[\text { Now }, \]
\[\text { If Rs . 80 is the SP, the MP = Rs } . 100\]
\[\text { If Re . 1 is the SP, the M . P = Rs } . \frac{100}{80}\]
\[\text { If Rs . 90 is the SP, the MP = Rs }. \left( \frac{100}{80} \times 90 \right) = Rs . 112 . 50\]
\[\text { Hence, the trader marks his goods at 12 . 5 % above the cost price } .\]
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