Question : A trader allows a trade discount of 20% and a cash discount of $6\frac{1}{4}$% on the marked price of the goods and gets a net gain of 20% of the cost. By how much above the cost should the goods be marked for sale?
Option 1: 40%
Option 2: 50%
Option 3: 60%
Option 4: 70%
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Correct Answer: 60%
Solution :
Given: A trader allows a tread discount of 20% and a cash discount of $6\frac{1}{4}=\frac{25}{4}$% on the marked price of the goods and gets a net gain of 20% of the cost.
Substitute the given values in the formula, net discount = $x+y-\frac{xy}{100}$%
$=20+\frac{25}{4}-\frac{20\times25}{100\times4}$
= $20+\frac{25-5}{4}=20+5$
$=25$%
According to the question,
Let the cost price be 100, then the selling price should be 120 with a profit of 20%.
So, marked price $= \frac{120}{75}×100 = 160$
So, the required percentage $= \frac{160-100}{100}\times100=60$%
Hence, the correct answer is $60$%.
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