Sometimes we come across certain types of questions in which shopkeeper sells the items at cost price and still he makes profit. This can only be possible if he gives less quantity to the customer than indicated. For example, if a shopkeeper sells milk at cost price but gives only 900 ml in a packet of 1 liter. In this case he is giving only 900 ml of milk but charging money from the customer that is equivalent to 1000 ml. Let the cost price of 900 ml of milk is 900k and that of 1000 ml of milk is 1000k, then for the shopkeeper, cost price and selling price are 900k and 1000k. 

\[\frac{{{\rm{SP}}}}{{{\rm{CP}}}}{\rm{ = }}\frac{{{\rm{Indicated}}\,\,{\rm{quantity}}}}{{{\rm{Actual}}\;{\rm{quantity}}}} = \frac{{1000}}{{900}} = \frac{{10}}{9}\]

Percentage Profit 

\[  \frac{{{\rm{SP}} - {\rm{CP}}}}{{{\rm{CP}}}} \times 100 = \frac{{\frac{{10}}{9} - 1}}{1} \times 100 = 11.11\% \]

Take another example, suppose a shopkeeper gives 20% less than the indicated weight but he also gives 10% discount. To calculate his profit / loss, suppose he purchased 100 units, while selling he gives only 80 units and claims 100 units. As he also offers 10% discount, he finally receives price of 90 units while actually selling only 80 units. 

Thus profit percentage = \(\frac{{90 - 80}}{{80}} \times 100 = 12.5\% \)

Always remember that indicated weight represents selling price while actual weight represents cost price.