A man sells two articles for 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. 1. 15 `2/3` %
B. 2. 16 `2/3` %
C. 3. 17 `1/3` %
D. 4. 18 `1/3` %

Answer

To solve the problem step by step, we will follow the reasoning outlined in the video transcript.

### Step-by-Step Solution:

1. **Understanding the Total Selling Price**:
The man sells two articles for ₹5000 each. Therefore, the total selling price (SP) for both articles is:
\[ SP = 5000 + 5000 = 10000 \]
Since he neither gains nor loses in the deal, the total cost price (CP) of both articles is also ₹10000.

2. **Identifying the Cost Price of Each Article**:
Let the cost price of the first article be \( CP_1 \) and the second article be \( CP_2 \). We know:
\[ CP_1 + CP_2 = 10000 \]

3. **Calculating the Selling Price of the First Article**:
The first article is sold at a gain of 25%. This means:
\[ SP_1 = CP_1 + 0.25 \times CP_1 = 1.25 \times CP_1 \]
Given that \( SP_1 = 5000 \):
\[ 1.25 \times CP_1 = 5000 \]
To find \( CP_1 \):
\[ CP_1 = \frac{5000}{1.25} = 4000 \]

4. **Finding the Cost Price of the Second Article**:
Now, using the total cost price:
\[ CP_1 + CP_2 = 10000 \]
Substituting \( CP_1 \):
\[ 4000 + CP_2 = 10000 \]
Therefore:
\[ CP_2 = 10000 - 4000 = 6000 \]

5. **Calculating the Loss on the Second Article**:
Since the first article was sold at a profit of ₹1000 (because \( SP_1 - CP_1 = 5000 - 4000 = 1000 \)), the second article must be sold at a loss of ₹1000 to ensure there is no overall profit or loss.

6. **Finding the Selling Price of the Second Article**:
The selling price of the second article (SP_2) is:
\[ SP_2 = CP_2 - \text{Loss} = 6000 - 1000 = 5000 \]

7. **Calculating the Loss Percentage**:
The loss incurred on the second article is ₹1000. To find the loss percentage:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{CP_2} \right) \times 100 = \left( \frac{1000}{6000} \right) \times 100 \]
Simplifying this:
\[ \text{Loss Percentage} = \frac{1}{6} \times 100 = 16.67\% \]
This can also be expressed as \( 16 \frac{2}{3}\% \).

### Final Answer:
The other article is sold at a loss of **16 2/3%**.