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Question
A shopkeeper allows 23% commision on his advertised price and still makes a profit of 10%. If he gains Rs 56 on one item, find his advertised price.
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Solution
\[\text { Let the CP of the item be Rs . x } . \]
\[\text { Profit = 10 % }\]
\[\text { SP = CP }\left( \frac{100 + \text { Profit % }}{100} \right)\]
\[SP = x\left( \frac{110}{100} \right)\]
\[\text { SP = Rs . 1 . 1x }\]
\[\text { Again, Profit = SP - CP }\]
\[\text { Therefore, Profit = Rs } . (1 . 1x - x)\]
\[ = Rs . 0 . 1x\]
We get,
0 . 1x = 56
x = Rs . 560
\[\text { Now, the advertised price }= \frac{1 . 1x}{1 - 0 . 23}\]
\[ = Rs . \frac{560 \times 1 . 1}{0 . 77}\]
\[ = Rs . 800\]
Therefore, the advertised price of the item is Rs . 800 .
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