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An article was sold after giving a discount on the marked price. What was the discount percentage given? I. The profit earned after giving the discount is 20%. Had the percentage of discount been doubled the seller would have incurred a loss of 4%. II. Marked price of the article is 60% above the cost price of the article.

An article was sold after giving a discount on the marked price. What was the discount percentage given? I. The profit earned after giving the discount is 20%. Had the percentage of discount been doubled the seller would have incurred a loss of 4%. II. Marked price of the article is 60% above the cost price of the article. Correct Answer if the data in statement (i) alone is sufficient to answer the question;

Let the Cost Price of an article be 100 and also let the discount percentage be x%.

According to equation (i):

Profit earned = 20%

∴ Selling Price = 120

Then, marked price × (100 – x)/100 = 120

⇒ Marked price = 12,000/(100 – x)      ----(a)

If the discount is doubled 

Loss incurred = 4%

∴ Selling Price = 96

Then, marked price × (100 – 2x)/100 = 96

⇒ Marked price = 9600/(100 – 2x)      ----(b)

Now by equation (a) and (b)

⇒ 12,000/(100 – x) = 9600/(100 – 2x)

⇒ 120/(100 – x) = 96/(100 – 2x)

⇒ 12000 – 240x = 9600 – 96x

⇒ 144x = 2400

⇒ x = 50/3 = 16.67%

∴ The data in statement (i) alone is sufficient to answer the question.

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