A man sells two articles for Rs.5000 each neither losing nor gaining in the deal. If he sold one of them at a gain of 25%, the other article is sold at a loss of

Options

A. 15`2/3`%
B. 16`2/3`%
C. 17`1/3`%
D. 18`1/3%

Answer

To solve the problem step by step, we need to determine the loss incurred on the second article when the first article is sold at a gain of 25%.

### Step 1: Understand the Selling Price
The man sells both articles for Rs. 5000 each. Therefore, the total selling price for both articles is:
- Selling Price (SP) of Article 1 = Rs. 5000
- Selling Price (SP) of Article 2 = Rs. 5000

### Step 2: Calculate the Cost Price of the First Article
Let’s denote the cost price of the first article as CP1. Since he sold the first article at a gain of 25%, we can express this as:
\[ SP1 = CP1 + 0.25 \times CP1 = 1.25 \times CP1 \]
Given that SP1 = Rs. 5000, we can set up the equation:
\[ 5000 = 1.25 \times CP1 \]
To find CP1, we rearrange the equation:
\[ CP1 = \frac{5000}{1.25} = 4000 \]
So, the cost price of the first article is Rs. 4000.

### Step 3: Calculate the Total Cost Price of Both Articles
Since he neither gains nor loses in the overall deal, the total cost price (CP) of both articles must equal the total selling price (SP) of both articles:
\[ Total SP = SP1 + SP2 = 5000 + 5000 = 10000 \]
Thus, the total cost price of both articles is also Rs. 10000.

### Step 4: Calculate the Cost Price of the Second Article
Let’s denote the cost price of the second article as CP2. We know:
\[ CP1 + CP2 = Total CP \]
Substituting the known values:
\[ 4000 + CP2 = 10000 \]
Now, solving for CP2:
\[ CP2 = 10000 - 4000 = 6000 \]
So, the cost price of the second article is Rs. 6000.

### Step 5: Calculate the Loss on the Second Article
The selling price of the second article is Rs. 5000, and its cost price is Rs. 6000. The loss incurred on the second article can be calculated as:
\[ Loss = CP2 - SP2 = 6000 - 5000 = 1000 \]

### Step 6: Calculate the Loss Percentage
The loss percentage can be calculated using the formula:
\[ Loss \% = \left( \frac{Loss}{CP2} \right) \times 100 \]
Substituting the known values:
\[ Loss \% = \left( \frac{1000}{6000} \right) \times 100 = \frac{1000 \times 100}{6000} = \frac{100000}{6000} = \frac{1000}{60} = \frac{50}{3} \approx 16.67\% \]

### Final Answer
The second article is sold at a loss of approximately 16.67%.

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