A shopkeeper allows his customers 10% off on the marked price of goods and still getsa profit of 12.5%. What is the actual cost of an article marked ₹2,750?

Correct option is B

Given:

Marked price = ₹2,750

Discount = 10%

Profit = 12.5%

Formula Used:

Selling price = Marked price − Discount

Profit = $$\frac{\text{Selling price} - \text{Cost price}}{\text{Cost price}} \times 100$$​​

Solution:

Let the cost price be C

Selling price after discount:

Selling price = $$2,750 \times \frac{90}{100} = ₹2,475$$​​

Now, using the profit percentage formula:

​$$12.5 = \frac{2,475 - C}{C} \times 100$$​​

​$$\frac{2,475 - C}{C} = \frac{12.5}{100}$$​​

​$$2,475 - C = 0.125 \times C$$​​

​$$C = \frac{2,475}{1.125} = ₹2,200$$

Alternate Solution: ​

​$$\frac{MP}{CP}=\frac{100+profit}{100-discount} \\ \ \\ \frac{2750}{CP}=\frac{112.5}{90}\\ \ \\ \implies CP = \frac{2750 \times 90}{112.5} =2200$$​​