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.

Answer 1

\[\text { Let the CP of the item be Rs . x } . \]

\[\text { Profit = 10 % }\]

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

\[SP = x\left( \frac{110}{100} \right)\]

\[\text { SP = Rs . 1 . 1x }\]

\[\text { Again, Profit = SP - CP }\]

\[\text { Therefore, Profit = Rs } . (1 . 1x - x)\]

\[ = Rs . 0 . 1x\]

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 .