A person purchases 50 mangoes at the same cost price per mango, sells 10 mangoes at a profit of 20%, sells another 20 mangoes at a profit of 30%, and the remaining mangoes get rotten and cannot be sold; what is the overall percentage profit or loss on the entire transaction?

Introduction / Context:
This question explores the concept of overall profit or loss when there are different selling prices for different parts of the same stock and some goods are wasted. In real life and in many exam problems, a seller does not always sell every item at the same profit percentage and some items may be spoiled or unsold. Calculating the combined effect on profit or loss requires careful use of cost price and selling price definitions.

Given Data / Assumptions:

• Total number of mangoes purchased = 50.
• All mangoes have the same cost price per piece.
• 10 mangoes are sold at 20% profit.
• 20 mangoes are sold at 30% profit.
• The remaining mangoes, which are 20 in number, get rotten and bring zero revenue.
• We need to find the overall profit or loss percentage on the full lot of 50 mangoes.

Concept / Approach:
The strategy is to work with a convenient assumed cost price per mango, calculate the total cost price of all mangoes, then compute the total selling price from all sales. The difference between total selling price and total cost price tells us whether there is profit or loss and by how much. Finally, the profit or loss percentage is calculated using the formula: (Profit or Loss / Total Cost Price) * 100. Since the cost per mango is the same, choosing a simple value like Re 1 makes the arithmetic easier without affecting the percentage.

Step-by-Step Solution:
Assume the cost price per mango is Re 1.Total cost price for 50 mangoes = 50 * 1 = Rs. 50.For 10 mangoes at 20% profit, selling price per mango = 1 * 1.20 = Rs. 1.20.Total selling price for these 10 mangoes = 10 * 1.20 = Rs. 12.For 20 mangoes at 30% profit, selling price per mango = 1 * 1.30 = Rs. 1.30.Total selling price for these 20 mangoes = 20 * 1.30 = Rs. 26.Remaining 20 mangoes are rotten and not sold, so their selling price is zero.Total selling price for all mangoes = 12 + 26 + 0 = Rs. 38.Total cost price is Rs. 50, so loss = 50 - 38 = Rs. 12.Loss percentage = (12 / 50) * 100 = 24% loss.

Verification / Alternative check:
The assumed cost price could be any convenient value. If we take cost price per mango as Rs. 2 instead, the total cost price becomes Rs. 100. Then selling price for 10 mangoes at 20% profit is 10 * 2.4 = Rs. 24, and for 20 mangoes at 30% profit is 20 * 2.6 = Rs. 52. Total selling price is Rs. 76, while total cost price is Rs. 100, so the loss is still Rs. 24, and the loss percentage is 24 / 100 * 100 = 24%. This confirms that the answer is independent of the assumed cost price value.

Why Other Options Are Wrong:
28% loss would require a larger absolute loss relative to the cost, which does not match the calculated difference of Rs. 12 if cost price per mango is Re 1.

26% and 22% loss values similarly do not fit the ratio of 12 to 50, which is exactly 0.24 and not any of those approximations.

Common Pitfalls:
Some learners wrongly compute separate profit percentages on the quantities sold and then average the percentages, ignoring the unsold rotten mangoes. Others forget that the items that get rotten still contribute to the cost price, even though they bring no revenue. Another typical confusion is whether to divide the net loss by the number of mangoes sold or by the total number purchased. The correct base for the percentage is always the total cost price of all purchased goods in such questions.

Final Answer:
The transaction results in an overall 24% loss on the mangoes.