The marked price of an article is 25% above its cost price. If it is sold for ₹450 with a profit of 6.4%, then the discount percent is closest to:

Given Data:

Profit percentage = 6.4%

Selling price = ₹450

The marked price is 25% above the cost price

Concept:

The problem involves the concept of profit and discount percentage calculation. The cost price and marked price of the article can be determined using the given information.

Then the discount percentage can be calculated.

Calculation:

CP = ₹450/(1 + 6.4/100) = ₹423.08 

⇒ The Marked Price (MP) is 25% more than the CP, which gives

MP = ₹423.08 × (1 + 25/100) = ₹528.85

⇒ Discount percentage can be found by subtracting SP from MP and dividing by MP, then multiplying by 100, which gives

Discount% = ((₹528.85 - ₹450)/₹528.85) ×  100 = 14.9%

∴ The discount percent is closest to 15%.

Shortcut Trick

We know that

\(\frac{MP}{CP}\) = \(\frac{100 +P}{100-D}\)

It is given that, MP of an article is 25% above its CP, and article is sold for ₹450 with a profit of 6.4%

Let the CP be 100 ⇒ SP = 125

\(\frac{125}{100}\) = \(\frac{100 +6.4}{100-D}\)

⇒ 12500 - 125D = 10640

⇒ 125D = 1860

⇒ D = 14.88 ≈ 15%