The percentage of loss when an article is sold at 50 is the same as that of the profit when it is sold at 70. The above-mentioned per centage of profit or loss on the article is

Options

A. 0.1
B. 16` 2/3` %
C. 0.2
D. 22 `2/3` %

Answer

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

### Step 1: Understand the Problem
We need to find the percentage of loss when an article is sold at 50 and the percentage of profit when it is sold at 70. According to the problem, these two percentages are equal.

### Step 2: Set Up the Cost Price (CP)
Let the cost price (CP) of the article be \( x \).

### Step 3: Calculate Loss Percentage at Selling Price (SP) of 50
When the article is sold at 50, the loss incurred can be expressed as:
\[ \text{Loss} = CP - SP = x - 50 \]
The loss percentage is given by:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{CP} \right) \times 100 = \left( \frac{x - 50}{x} \right) \times 100 \]

### Step 4: Calculate Profit Percentage at Selling Price (SP) of 70
When the article is sold at 70, the profit can be expressed as:
\[ \text{Profit} = SP - CP = 70 - x \]
The profit percentage is given by:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{70 - x}{x} \right) \times 100 \]

### Step 5: Set the Loss Percentage Equal to the Profit Percentage
According to the problem, the loss percentage at 50 is equal to the profit percentage at 70:
\[ \left( \frac{x - 50}{x} \right) \times 100 = \left( \frac{70 - x}{x} \right) \times 100 \]

### Step 6: Simplify the Equation
We can cancel out the 100 from both sides:
\[ \frac{x - 50}{x} = \frac{70 - x}{x} \]
Cross-multiplying gives:
\[ x - 50 = 70 - x \]

### Step 7: Solve for x
Now, we can solve for \( x \):
\[ x + x = 70 + 50 \]
\[ 2x = 120 \]
\[ x = 60 \]

### Step 8: Calculate the Loss Percentage
Now that we have the cost price \( x = 60 \), we can calculate the loss percentage when sold at 50:
\[ \text{Loss} = 60 - 50 = 10 \]
\[ \text{Loss Percentage} = \left( \frac{10}{60} \right) \times 100 = \frac{1000}{60} = \frac{100}{6} = \frac{50}{3} \approx 16.67\% \]

### Step 9: Conclusion
The percentage of profit or loss on the article is \( \frac{50}{3} \% \) or approximately \( 16.67\% \).

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