A retailer would have made a profit of 18% if he sold an article at its marked price. If he allowed a discount of 10% on the marked price, what would his actual profit on that article have been?

Correct option is A

Given:

A retailer would have made a profit of 18% if he sold an article at its marked price

Formula used:

​$$M = C \times \left(1 + \frac{\text{Profit Percentage at Marked Price}}{100}\right)$$

where C is cost price , M is marked price , S is selling price

​$$S = M \times \left(1 - \frac{\text{Discount Percentage}}{100}\right)$$

Solution:

If Cost Price (C): Rs. 100

Profit Percentage at Marked Price: 18%

Discount on Marked Price: 10%

Calculate the Marked Price:

​$$M = 100 \times \left(1 + \frac{18}{100}\right) = 100 \times 1.18 = 118 \, \text{Rs.}$$

​​Calculate the Selling Price:

​$$S = 118 \times \left(1 - \frac{10}{100}\right) = 118 \times 0.90 = 106.2 \, \text{Rs.}$$

​​Calculate the Profit

Profit = SP - CP 

Profit = 106.2-100 = 6.2

Profit Percentage = $$\frac{\text{Profit}}{C} \times 100$$

​​$$\text{Profit Percentage} = \frac{6.2}{100} \times 100 = 6.2\%.$$

The profit percentage after allowing a 10% discount is 6.2%

Thus, correct option is (a)