Question:medium
A man sold \(\frac{3}{5}\)th of his articles at a gain of 20% and the remaining at cost price. Find the percentage gain earned in the transaction.
A man sold \(\frac{3}{5}\)th of his articles at a gain of 20% and the remaining at cost price. Find the percentage gain earned in the transaction.
Show Hint
Use the alligation (weighted average) formula with the two gain rates and their weights.
Updated On: Jul 30, 2026
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The Correct Option is C
Solution and Explanation
Step 1: Pick a convenient number of articles.
Assume the man has 5 articles, each with a cost price of Rs. 1, so the total cost price is Rs. 5.
Step 2: Find the selling price of each part.
He sells $\frac{3}{5}$ of 5, that is 3 articles, at a 20% gain: selling price $= 3 \times 1 \times 1.20 = \text{Rs. } 3.60$. He sells the remaining 2 articles at cost price: selling price $= 2 \times 1 = \text{Rs. } 2$.
Step 3: Find the total selling price and the gain.
Total selling price $= 3.60 + 2 = \text{Rs. } 5.60$. Total gain $= 5.60 - 5 = \text{Rs. } 0.60$.
Step 4: Convert the gain to a percentage of the cost price.
Gain percentage $= \dfrac{0.60}{5} \times 100 = 12\%$.
Final Answer:
Using real numbers instead of the alligation formula gives the same 12% gain. \[ \boxed{12\%} \]
Assume the man has 5 articles, each with a cost price of Rs. 1, so the total cost price is Rs. 5.
Step 2: Find the selling price of each part.
He sells $\frac{3}{5}$ of 5, that is 3 articles, at a 20% gain: selling price $= 3 \times 1 \times 1.20 = \text{Rs. } 3.60$. He sells the remaining 2 articles at cost price: selling price $= 2 \times 1 = \text{Rs. } 2$.
Step 3: Find the total selling price and the gain.
Total selling price $= 3.60 + 2 = \text{Rs. } 5.60$. Total gain $= 5.60 - 5 = \text{Rs. } 0.60$.
Step 4: Convert the gain to a percentage of the cost price.
Gain percentage $= \dfrac{0.60}{5} \times 100 = 12\%$.
Final Answer:
Using real numbers instead of the alligation formula gives the same 12% gain. \[ \boxed{12\%} \]
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