Question : A treader wishes to gain 20% after allowing a 10% discount on the marked price to his customers. At what percent higher than the cost price must he mark up his goods?
Option 1: $30\%$
Option 2: $33\frac{1}{3}\%$
Option 3: $34\frac{2}{3}\%$
Option 4: $35\%$
Correct Answer: $33\frac{1}{3}\%$
Solution :
Let's denote the cost price as CP, the marked price as MP and the selling price as SP.
The trader wants to gain 20% after allowing a 10% discount on the marked price.
This means that the selling price is 90% of the marked price (100% – 10%), and this selling price is 120% of the cost price (100% + 20%).
SP = 0.9 MP = 1.2 CP
We can rearrange this to find MP in terms of CP:
MP = $\frac{1.2 \text{CP}}{0.9} = \frac{4}{3}\text{CP}$
This means that the marked price is $\frac{4}{3}$ times the cost price.
$\therefore$ Required percentage $=\frac{\text{MP – CP}}{\text{CP}}×100=\frac{4-3}{3}×100 = 33\frac{1}{3}$%
Hence, the correct answer is $33\frac{1}{3}\%$.
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