Question

A trader sold half of his articles at 60% profit, half of the remaining at 20% loss and the rest was sold at the cost price. In total transaction his gain % or loss % will be:

• A. Gain 20%
• B. Loss 5%
• C. Gain 40%
• D. Gain 25%

Answer 1

The Correct Option is D

To solve this problem, let's break down the transactions of the trader:

1. Suppose the trader has n articles.
2. He sold half of his articles, which is n/2, at a 60% profit. Profit from these articles is
   Profit = Cost Price × 60%
   So, the Selling Price (SP) for these articles is
   SP = Cost Price × (1 + 60/100) = 1.6 × Cost Price.
3. The remaining articles are n/2. Out of these, half are sold at a 20% loss and half at cost price.
4. Thus, n/4 articles are sold at a 20% loss. So, the Selling Price for these articles is
   SP = Cost Price × (1 - 20/100) = 0.8 × Cost Price.
5. The rest, n/4 articles, are sold at the cost price (no profit, no loss), so
   SP = Cost Price.

Now, calculate the total cost price (CP) and total selling price (SP):

• Total CP = n × Cost Price.
• Total SP = (n/2 × 1.6 × Cost Price) + (n/4 × 0.8 × Cost Price) + (n/4 × Cost Price).

Let's simplify the SP expression:

• Total SP = (0.8n × Cost Price) + (0.2n × Cost Price) + (0.25n × Cost Price).

Total SP = (0.8+0.2+0.25)n × Cost Price = 1.25n × Cost Price.

The percentage gain or loss is given by:
Percentage Gain/Loss = ((Total SP - Total CP) / Total CP) × 100%

• Percentage Gain = ((1.25n × Cost Price - n × Cost Price) / (n × Cost Price)) × 100%.

Simplifying:

• Percentage Gain = (0.25n × Cost Price / n × Cost Price) × 100% = 0.25 × 100% = 25%.

Thus, the correct answer is Gain 25%.