Calculating Profit Percentage When Selling Price is 6/5 Times the Cost Price

Understanding the relationship between the cost price (CP) and the selling price (SP) is a fundamental concept in basic mathematics and business calculations. If the selling price of an article is 6/5 times of its cost price, what is the profit percentage?

Mathematical Derivation

Let the cost price (CP) of an article be x. The selling price (SP) is given by (frac{6}{5}x).

Therefore, the gain can be calculated as:

[text{Gain} SP - CP frac{6}{5}x - x frac{6x - 5x}{5} frac{x}{5}]

The gain percentage is calculated as:

[text{Gain Percentage} left(frac{text{Gain}}{CP}right) times 100 left(frac{frac{x}{5}}{x}right) times 100 left(frac{1}{5}right) times 100 20%]

Solutions and Examples

Solution 1:

Let the cost price (CP) of an article be x. The selling price (SP) is given by (frac{6}{5}x).

The gain can be calculated as:

[text{Gain} SP - CP frac{6}{5}x - x frac{6x - 5x}{5} frac{x}{5}]

Thus, the gain percentage is:

[text{Gain Percentage} left(frac{frac{x}{5}}{x}right) times 100 left(frac{1}{5}right) times 100 20%]

Solution 2:

Let the cost price (CP) be Rs. 100. Then the selling price (SP) is (frac{6}{5} times 100 120).

The gain can be calculated as:

[text{Gain} SP - CP 120 - 100 20]

Thus, the gain percentage is:

[text{Gain Percentage} left(frac{20}{100}right) times 100 20%]

Conclusion

As shown by the above solutions, if the selling price of an article is 6/5 times its cost price, the profit percentage is always 20 percent. This concept is crucial for understanding the basics of sales and profit calculations in business mathematics.

Understanding these calculations can also help in analyzing different pricing strategies and making informed business decisions.