An article was marked at ₹11,500. A discount of 25% was offered, resulting in a profit of15%. What is the cost price of the article?

Correct option is B

Given:

Marked price of the article = ₹11,500

Discount offered = 25%

Profit = 15%

Formula Used:

Selling Price = $$\text{Marked Price} \times (1 - \frac{\text{Discount}}{100})$$​​

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

Solution:

Let the cost price of the article be C

Selling Price after 25% discount:

Selling Price = $$11,500 \times \left(1 - \frac{25}{100}\right)$$​​

​$$= 11,500 \times 0.75 = ₹8,625​$$​​

Profit = 15%, So

​$$\frac{8,625 - C}{C} \times 100 = 15​$$​​

​$$\frac{8,625 - C}{C} = \frac{15}{100}$$​​

8,625 - C = 0.15C

8,625 = 1.15C

C = $$\frac{8,625}{1.15}$$​ = ₹7,500

Alternate Solution: ​

​$$\frac{MP}{CP} = \frac{100+profit\%}{100 - discount\%} \\ \ \\ \frac{11500}{CP}= \frac{115}{75} \\ \ \\ \implies CP = \frac{11500 \times 75}{115} = 7500$$​​