mr. rajesh calculates his profit percentage as a percentage of selling price. he sells an item for rs.150 and calculates his profit percentage to be 20% what is the true profit percentage
25%
(20×150) ÷100=30=profit, profit℅=(30×100) ÷120 =25℅ Hints=[cp=150-30=120]
To find the true profit percentage, we need to calculate it as a percentage of the cost price.
Here's how you can do it step-by-step:
1. Let's assume the cost price of the item is "x" rupees.
2. We know that the selling price (SP) is Rs. 150.
3. The profit percentage is calculated as the difference between the selling price and cost price, divided by the cost price, multiplied by 100.
Profit Percentage = ((Selling Price - Cost Price) / Cost Price) * 100
Let's substitute the given values:
Profit Percentage = ((150 - x) / x) * 100
Now, we are told that Mr. Rajesh calculated his profit percentage as 20% of the selling price, which means:
Profit Percentage = 20% of Selling Price
Profit Percentage = (20/100) * 150
Profit Percentage = 30
Since Mr. Rajesh calculated the profit percentage as 20%, this means that (150 - x) / x * 100 = 20.
Now, we just need to solve this equation to find the true profit percentage.
Simplifying the equation:
(150 - x) / x = 20 / 100
(150 - x) / x = 1 / 5
Cross-multiplying:
5(150 - x) = x
750 - 5x = x
750 = 6x
x = 125
So, the cost price (CP) is Rs. 125.
Now, let's substitute the value of CP into the profit percentage formula to find the true profit percentage:
Profit Percentage = (150 - 125) / 125 * 100
Profit Percentage = 25 / 125 * 100
Profit Percentage = 20
Therefore, the true profit percentage is 20%.