A trader sold an article for N150 and made a profit of 20%. What was the cost price of the article
Show workings bit by bit
Let's start with the formula for calculating profit:
Profit = Selling Price - Cost Price
We know the selling price is N150 and the profit is 20% of the cost price. So we can set up the equation:
0.2x = Selling Price - Cost Price
0.2x = N150 - Cost Price
Now we can substitute the given profit margin percentage into the equation:
0.2x = 0.20x
So we have:
0.2x = N150 - Cost Price
0.20x = Cost Price
Now we can solve for the cost price:
0.20x = Cost Price
x = Cost Price / 0.20
x = 750
Therefore, the cost price of the article was N750.
To verify our answer, we can calculate the profit:
Profit = Selling Price - Cost Price
Profit = N150 - N750
Profit = N-600
Now we can calculate the profit margin percentage:
Profit Margin Percentage = (Profit / Cost Price) x 100%
Profit Margin Percentage = (-600 / 750) x 100%
Profit Margin Percentage = -80%
This indicates that our calculation is correct, as we have a negative profit margin percentage, which means a loss. However, we know from the problem statement that the trader made a profit, so we can conclude that our calculation for the profit is incorrect and we need to re-examine the problem.
Step 1: Convert the profit percentage to a decimal.
To convert 20% to a decimal, divide it by 100:
20 / 100 = 0.20
Step 2: Calculate the selling price.
The selling price is given as N150.
Step 3: Calculate the cost price.
Let's assume the cost price is represented by C.
Since the profit percentage is 20%, the profit made can be calculated as 20% of the cost price (0.20 * C).
So, the selling price equals the cost price plus the profit:
N150 = C + 0.20C
Step 4: Combine like terms.
Combine the cost price and the profit:
N150 = 1.20C
Step 5: Solve for the cost price.
Divide both sides of the equation by 1.20 to isolate C:
N150 / 1.20 = C
Step 6: Perform the calculation.
Divide N150 by 1.20:
N125 = C
Step 7: Answer
The cost price of the article was N125.