Problem Breakdown: Two Articles Transaction

This problem requires us to calculate the loss percentage on one of two articles sold. We know that both articles were sold for the same price (Rs. 3,000 each) and that the overall transaction resulted in neither profit nor loss. We are also given that the first article was sold at a profit of 25%.

Calculating Cost Price of the First Article

Let's denote the Selling Price (SP) of the first article as $SP_1$ and its Cost Price (CP) as $C_1$. The profit percentage for the first article is given as 25%.

• Given Selling Price: $SP_1 = 3000$ rupees
• Given Profit percentage = 25%
• The relationship between Selling Price, Cost Price, and Profit Percentage is: $SP = CP \times (1 + \frac{\text{Profit Percentage}}{100})$
• Plugging in the values for the first article: $3000 = C_1 \times (1 + \frac{25}{100})$
• Simplifying the expression: $3000 = C_1 \times (1 + 0.25)$
• $3000 = C_1 \times 1.25$
• To find the Cost Price $C_1$, we rearrange the equation: $C_1 = \frac{3000}{1.25}$
• Calculating the value: $C_1 = \frac{3000}{5/4} = 3000 \times \frac{4}{5} = 600 \times 4 = 2400$

Therefore, the Cost Price of the first article was Rs. 2,400.

Determining Cost Price of the Second Article

Let the Selling Price of the second article be $SP_2$ and its Cost Price be $C_2$.

• Given Selling Price: $SP_2 = 3000$ rupees
• The condition of "no loss and profit in the entire transaction" means that the Total Selling Price must equal the Total Cost Price.
• Total Selling Price = $SP_1 + SP_2 = 3000 + 3000 = 6000$ rupees
• Total Cost Price = Total Selling Price = 6000 rupees
• The Total Cost Price is also the sum of the individual cost prices: Total CP = $C_1 + C_2$
• We know $C_1 = 2400$, so we can substitute this into the equation: $6000 = 2400 + C_2$
• Solving for $C_2$: $C_2 = 6000 - 2400 = 3600$

Thus, the Cost Price of the second article was Rs. 3,600.

Calculating Loss Incurred on the Second Article

Now, we need to calculate the loss percentage specifically for the second article.

• Cost Price of the second article ($C_2$) = Rs. 3,600
• Selling Price of the second article ($SP_2$) = Rs. 3,000
• Since the Cost Price (Rs. 3,600) is greater than the Selling Price (Rs. 3,000), there is a loss.
• Loss Amount = Cost Price - Selling Price = $C_2 - SP_2$
• Loss Amount = $3600 - 3000 = 600$ rupees
• The formula to calculate the loss percentage is: $\text{Loss Percentage} = \frac{\text{Loss Amount}}{C_2} \times 100$
• Substituting the calculated values: $\text{Loss Percentage} = \frac{600}{3600} \times 100$
• Simplifying the fraction: $\text{Loss Percentage} = \frac{1}{6} \times 100$
• $\text{Loss Percentage} = \frac{100}{6}\% = \frac{50}{3}\%$
• Converting the improper fraction to a mixed number: $\frac{50}{3}\% = 16\frac{2}{3}\%$

Final Answer Explanation

The loss incurred on the second article is calculated to be $16\frac{2}{3}\%$.