Question

A dealer sold three-fourth of his articles at a gain of 20% and the remaining at cost price. What is the gain earned by him in the whole transaction?

• A. 13\%
• B. 16\%
• C. 10\%
• D. 12\%

Hint:

For mixed gain and loss problems, break the transactions into smaller parts based on the gain or loss percentages for each group and calculate the total gain accordingly.

Answer 1

The Correct Option is B

Step 1: Let the cost price of each article be \( C \).
Assume the total number of articles is 1 (for simplicity). Step 2: Articles sold at a gain of 20\%
Three-fourths of the articles are sold at a gain of 20\%. The selling price of each article in this group is \( C \times 1.20 \). So, the total selling price for three-fourths of the articles is: \[ \text{Selling price of } \frac{3}{4} \text{ of the articles} = \frac{3}{4} \times C \times 1.20 = 0.90C \] Step 3: Articles sold at cost price
The remaining one-fourth of the articles are sold at cost price, so the total selling price of this group is: \[ \text{Selling price of } \frac{1}{4} \text{ of the articles} = \frac{1}{4} \times C = 0.25C \] Step 4: Total selling price
The total selling price for all articles is: \[ \text{Total selling price} = 0.90C + 0.25C = 1.15C \] Step 5: Total cost price
The total cost price of all the articles is: \[ \text{Total cost price} = C \] Step 6: Total gain
The total gain is the difference between the total selling price and the total cost price: \[ \text{Total gain} = 1.15C - C = 0.15C \] Step 7: Percentage gain
The percentage gain is calculated as: \[ \text{Percentage gain} = \frac{0.15C}{C} \times 100 = 16\% \] Thus, the gain earned by the dealer is \( 16\% \).