A wholesaler has 200 dozens of mangoes. He sells some of these mangoes at a profit of 20% and the remaining mangoes at a profit of 10%, so that his overall profit on all the mangoes is 13%. How many dozens of mangoes does he sell at 20% profit?

Introduction / Context:
This is a mixture or weighted average type question in the context of profit and loss. The wholesaler sells part of his stock at a higher profit percentage and the rest at a lower profit percentage, and the combined effect is given as an overall profit percentage. We are required to find how many dozens were sold at the higher rate of profit. This pattern is very frequent in aptitude exams.

Given Data / Assumptions:

• Total stock = 200 dozens of mangoes.
• Some dozens sold at 20% profit.
• Remaining dozens sold at 10% profit.
• Overall profit on all mangoes = 13%.
• Cost price per dozen is uniform.
• We need the number of dozens sold at 20% profit.

Concept / Approach:
Assume cost price per dozen is C. Let x be the number of dozens sold at 20% profit:

• Profit from x dozens at 20% = 0.2Cx.
• Remaining dozens = 200 - x, profit on them = 0.1C(200 - x).
• Total profit on 200 dozens at 13% = 0.13 * 200C.

We then set the total profit from both parts equal to the overall profit and solve for x.

Step-by-Step Solution:
Let x be the number of dozens sold at 20% profit. Then 200 - x dozens are sold at 10% profit. Assume cost price per dozen is C. Profit from x dozens at 20% = 0.2Cx. Profit from 200 - x dozens at 10% = 0.1C(200 - x). Total profit at 13% on all 200 dozens = 0.13 * 200C. Set up equation: 0.2Cx + 0.1C(200 - x) = 0.13 * 200C. Divide by C: 0.2x + 0.1(200 - x) = 0.13 * 200. 0.2x + 20 - 0.1x = 26. 0.1x = 6, so x = 60. Thus, 60 dozens are sold at 20% profit.

Verification / Alternative check:
Take cost price per dozen as 1 for simplicity:

• 60 dozens at 20% profit give profit = 60 * 0.2 = 12.
• 140 dozens at 10% profit give profit = 140 * 0.1 = 14.
• Total profit = 12 + 14 = 26.
• Total cost = 200 * 1 = 200.
• Overall profit percent = (26 / 200) * 100 = 13%.

This matches the overall profit given in the question, so our solution is correct.

Why Other Options Are Wrong:
If 140 dozens were at 20%, the overall profit would be much higher than 13%. With 80, 120, or 100 dozens at 20%, the blended profit would differ from 13% when computed correctly. Only 60 dozens at 20% and 140 dozens at 10% give the required 13% overall profit on 200 dozens.

Common Pitfalls:
One common issue is to average 20% and 10% directly as 15% and then attempt to adjust without considering quantities. Another mistake is in forming the equation and putting the wrong coefficient on x or 200 - x. Always write the total profit as the sum of profits from both groups and equate it to the overall profit on the full 200 dozens.

Final Answer:
The wholesaler sells 60 dozens of mangoes at 20% profit.