Tade bought 200 mangoes at 4 for ₦2.50. 30 out of the mangoes got spoilt and the remaining were sold at 2 for ₦2.40. Find the percentage profit or loss.

1. Analyze the question

We need to determine the total cost price (CP) of the mangoes, the total selling price (SP) after accounting for the spoilt ones, and then calculate the percentage profit or loss using the formula:

2. Explain the concept

• Cost Price (CP): The total amount spent to acquire the goods.
• Selling Price (SP): The total amount received from selling the goods.
• Profit: Occurs when SP > CP (Profit = SP - CP).
• Loss: Occurs when CP > SP (Loss = CP - SP).

3. Show the solution

Step 1: Calculate the Total Cost Price (CP) Tade bought 200 mangoes at 4 for ₦2.50.

• Number of groups of 4 in 200 = $200 \div 4 = 50$ groups.
• Total CP = $50 \times ₦2.50 = ₦125.00$.

Step 2: Calculate the Total Selling Price (SP)

• Number of good mangoes = $200 - 30 = 170$ mangoes.
• They were sold at 2 for ₦2.40.
• Number of groups of 2 in 170 = $170 \div 2 = 85$ groups.
• Total SP = $85 \times ₦2.40 = ₦204.00$.

Step 3: Determine Profit or Loss Since the SP (₦204.00) is greater than the CP (₦125.00), Tade made a profit.

• Profit = $₦204.00 - ₦125.00 = ₦79.00$.

Step 4: Calculate Percentage Profit

• Percentage Profit = $\frac{\text{Profit}}{\text{CP}} \times 100\%$
• Percentage Profit = $\frac{79}{125} \times 100\%$
• Percentage Profit = $0.632 \times 100\% = 63.2\%$.

4. Identify the answer

Comparing our result to the options provided, we see that 63.2% profit matches option C.

5. Tip

When dealing with "items per price" questions, always find the cost/selling price of a single unit first if the numbers are complex, or group them as we did above. Also, always double-check if the question asks for the percentage of the Cost Price (which is standard) or the Selling Price, as this is a common trap in JAMB questions!