Profit Percentage at Market Price: Cracking the Discount and Gain Formula

Understanding how profit percentages work at market price versus discounted prices can provide great insights into pricing strategies. Let's delve into a detailed explanation of how to calculate the profit percentage if an article is sold at its market price, with no discount applied.

Introduction to the Problem

Imagine a scenario where a shopkeeper allows a discount of 25% on the market price of a table and still manages to make a profit of 20% on the cost price. The question here is, what would be the profit percentage if the table were sold at its market price without any discount?

The Given Scenario

Let the marked price (M.P.) of the article be Rs. 100. After allowing a 25% discount, the selling price (S.P.) becomes:

S.P. M.P. - (Discount % of M.P.) 100 - (25% of 100) 100 - 25 Rs. 75.

Since the shopkeeper has made a 20% profit on the cost price (C.P.), we need to calculate the C.P. first. We know that:

Profit S.P. - C.P.
20% of C.P. 75 - C.P.
C.P. 75 / (1 20/100) 75 / 1.20 Rs. 62.50.

Profit if Sold at Market Price

Now, if the table is sold at the marked price (Rs. 100) with no discount, the profit can be calculated as:

Profit S.P. - C.P.
100 - 62.50 Rs. 37.50.

The profit percentage can be calculated using the formula:

Profit Percent (Profit / C.P.) * 100.
(37.50 / 62.50) * 100 60%.

Alternative Calculation Using Formulas

We can use the following formula to directly calculate the profit percentage:

M.P./C.P. (100 P) / (100 - D), where P is the profit percentage and D is the discount percentage.

Plugging in the values, we get:

M.P./C.P. (100 20) / (100 - 25) 120 / 75 1.60.

So, if the marked price is Rs. 100, the cost price becomes Rs. 62.50. If the article is sold at its market price, the profit will be:

Profit M.P. - C.P.
100 - 62.50 Rs. 37.50.

And the profit percent is:

Profit Percent (37.50 / 62.50) * 100 60%.

Conclusion

Through these calculations, we have determined that if an article is sold at its marked price with no discount, the profit percentage would be 60%. This method can be applied to any similar problems, making it a powerful tool in understanding pricing and profit margins.