A shopkeeper buys 4 mangoes for Rs. 6 and sells them at a rate of 4 mangoes for Rs. 4. What is the percentage of profit or loss made by the shopkeeper on this transaction?

Introduction / Context:
This is a basic profit and loss question involving unitary method. Instead of directly giving the cost price or selling price of one item, the question gives the price for a group of identical items. To find the exact profit or loss percentage, we convert these group prices into per unit cost and per unit selling price and then compare them.

Given Data / Assumptions:

• Buying rate: 4 mangoes for Rs. 6.
• Selling rate: 4 mangoes for Rs. 4.
• Mangoes are identical and of the same quality.
• We assume there are no extra expenses such as transport or wastage.
• The objective is to find whether there is a profit or a loss and its percentage.

Concept / Approach:
Profit or loss percentage is always calculated on the cost price. First, find the cost price of one mango by dividing the total cost by the number of mangoes bought. Then, find the selling price of one mango in the same way. By comparing the selling price with the cost price, we decide whether this is a profit or a loss. Finally, we use the formula for percentage loss or profit based on the difference between cost and selling prices.

Step-by-Step Solution:
Step 1: Cost price (CP) of 4 mangoes = Rs. 6. Step 2: CP of 1 mango = 6 / 4 = Rs. 1.50. Step 3: Selling price (SP) of 4 mangoes = Rs. 4. Step 4: SP of 1 mango = 4 / 4 = Rs. 1.00. Step 5: Since SP < CP, the shopkeeper incurs a loss. Step 6: Loss per mango = CP - SP = 1.50 - 1.00 = Rs. 0.50. Step 7: Loss percentage = (Loss / CP) * 100 = (0.50 / 1.50) * 100. Step 8: Simplify: 0.50 / 1.50 = 1/3, so loss percentage = (1/3) * 100 = 33.333% (approximately).

Verification / Alternative check:
Consider buying and selling 12 mangoes to avoid fractions. CP for 12 mangoes = 3 sets of 4 mangoes = 3 * Rs. 6 = Rs. 18. SP for 12 mangoes = 3 sets of 4 mangoes sold = 3 * Rs. 4 = Rs. 12. Loss on 12 mangoes = 18 - 12 = Rs. 6. Loss percentage = (6 / 18) * 100 = 33.333%, which confirms the earlier calculation.

Why Other Options Are Wrong:
Loss percentages like 36.333%, 33.666% or 36.666% do not match the exact fraction 1/3 of the cost price. The option 25.000% is much smaller than the true value. Only 33.333% is consistent with both unitary method and scaled computation using 12 mangoes.

Common Pitfalls:
Some learners mistakenly compute profit or loss on the selling price instead of the cost price, or mix up the two group rates. Others average 6 and 4 or compare the groups directly without converting to per unit values. Always reduce the situation to one item and then apply the correct percentage formula to get accurate results.

Final Answer:
The shopkeeper makes a 33.333% loss on selling the mangoes.