Math CentralQuandaries & Queries


Question from edward, a student:

A shopkeeper marks his goods to gain 35%. He allows 10% discount for cash payment. What is his profit percent when he sells the goods for cash?

Hi Edward,

Suppose the storekeeper has some good that cost him $\$C.$ If he marks up his goods to gain $35\%$ then he adds $35\%$ of $\$C$ to $\$C$ to obtain the selling price. This the selling price $\$S$ is given by

\[\$S = \$C + 0.35 \times $C = 1.35 \times \$C.\]

If you pay cash then you get a $10\%$ discount so to you the selling price is $\$S - 0.10 \times \$S = 0.90 \times \$S.$ In this case what is his profit as a percentage of $\$C?$


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