Three varieties of mangoes, M, N and O, have cost prices Rs 20 per kg, Rs 40 per kg and Rs 50 per kg respectively. They are mixed in the ratio 2 : 3 : 5 to form a 1 kg mixture. At what selling price per kg should the mixture be sold to earn an overall profit of 20%?

Introduction / Context:
Mixture problems with profit and loss are very popular in quantitative aptitude. Here, three types of mangoes have different cost prices and are mixed in a fixed ratio. We must first compute the average cost of the mixture per kilogram and then add a desired profit percentage to find the selling price. This teaches how weighted averages and profit percentages work together.

Given Data / Assumptions:

• Type M costs Rs 20 per kg.
• Type N costs Rs 40 per kg.
• Type O costs Rs 50 per kg.
• They are mixed in the ratio M : N : O = 2 : 3 : 5.
• Required profit on the mixture = 20% over cost.
• We need selling price per kg of the final mixture.

Concept / Approach:
Because the mixture is in the ratio 2 : 3 : 5, we can assume a convenient total weight, say 10 kg (2 + 3 + 5). We then compute the total cost for these 10 kg, divide by 10 to find cost per kg, and finally multiply by 1.2 to account for a 20% profit. This method uses the idea of weighted average and ensures all three varieties are correctly included in the cost.

Step-by-Step Solution:
Step 1: Assume total mixture = 2 + 3 + 5 = 10 kg.Step 2: Cost of M in the mixture = 2 kg * Rs 20/kg = Rs 40.Step 3: Cost of N in the mixture = 3 kg * Rs 40/kg = Rs 120.Step 4: Cost of O in the mixture = 5 kg * Rs 50/kg = Rs 250.Step 5: Total cost for 10 kg = 40 + 120 + 250 = Rs 410, so cost per kg = 410 / 10 = Rs 41.Step 6: To earn 20% profit, SP per kg = 41 * 1.2 = Rs 49.2.

Verification / Alternative check:
If 10 kg of mixture cost Rs 410, then selling 10 kg at Rs 49.2 per kg gives revenue of 10 * 49.2 = Rs 492. Profit = 492 - 410 = Rs 82. Profit percentage = (82 / 410) * 100 = 20%. This matches the required profit and confirms both the average cost and final selling price per kg are correct.

Why Other Options Are Wrong:
Rs 47, Rs 48.5 and Rs 50.3 correspond to profit percentages different from 20%. Some may give less than 20%, others more. For instance, selling at Rs 47 would clearly yield a profit of only (47 - 41)/41 ≈ 14.63%. Selling at Rs 50.3 gives a profit of about 22.8%. Therefore, only Rs 49.2 satisfies the 20% profit condition exactly.

Common Pitfalls:
Common mistakes include taking the simple average of 20, 40 and 50 without weighting them by the ratio, or misinterpreting 20% profit as 20 rupees added. Another frequent error is to compute the profit percentage on selling price instead of cost price. Always use a weighted average for mixtures and then apply profit, profit% = (SP - CP) / CP * 100.

Final Answer:
The shopkeeper should sell the mango mixture at Rs. 49.2 per kg to earn a 20% profit.