A shopkeeper sold two articles at Rs. 12,000 each. He sold one article at a profit of 20% and the other one at a loss of 20%. What is the net gain or loss to the shop keeper?
A loss of Rs. 1000
To solve the problem, we need to calculate the cost price for both articles and determine if there's a net profit or loss in overall transactions.
Let's denote:
- \(SP_1 = SP_2 = 12,000 \text{ Rs}\) (Selling Price of each article)
- \(CP_1\) : Cost Price of the first article.
- \(CP_2\) : Cost Price of the second article.
Article 1:
The first article is sold at a profit of 20%. Therefore,
\(SP_1 = CP_1 \times \left(1 + \frac{20}{100}\right) = CP_1 \times 1.2\)
Given \(SP_1 = 12,000 \text{ Rs}\), we have:
\(1.2 \times CP_1 = 12,000\)
\(CP_1 = \frac{12,000}{1.2} = 10,000 \text{ Rs}\)
Article 2:
The second article is sold at a loss of 20%. Therefore,
\(SP_2 = CP_2 \times \left(1 - \frac{20}{100}\right) = CP_2 \times 0.8\)
Given \(SP_2 = 12,000 \text{ Rs}\), we have:
\(0.8 \times CP_2 = 12,000\)
\(CP_2 = \frac{12,000}{0.8} = 15,000 \text{ Rs}\)
Calculating Net Gain or Loss:
- Total Cost Price, \(CP = CP_1 + CP_2 = 10,000 + 15,000 = 25,000 \text{ Rs}\)
- Total Selling Price, \(SP = SP_1 + SP_2 = 12,000 + 12,000 = 24,000 \text{ Rs}\)
The net loss is calculated as:
\(\text{Net Loss} = CP - SP = 25,000 - 24,000 = 1,000 \text{ Rs}\)
Thus, the shopkeeper incurs a net loss of Rs. 1,000.
The correct answer is: A loss of Rs. 1000
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