If an article is sold at 12.5% gain instead of 162/3% loss the man gains Rs 1533 more find the CP of that article.

Options

A. 5256
B. 4599
C. 5688
D. 5292

Answer

To find the cost price (CP) of the article based on the information provided, we can follow these steps:

### Step 1: Understand the Gain and Loss Percentages
- The article is sold at a gain of 12.5%.
- If it were sold at a loss of \( \frac{50}{3} \% \) (which is approximately 16.67%), the man would have gained Rs 1533 less.

### Step 2: Convert Percentages to Decimal Form
- Gain of 12.5% can be expressed as \( \frac{12.5}{100} = 0.125 \).
- Loss of \( \frac{50}{3} \% \) can be expressed as \( \frac{16.67}{100} \approx 0.1667 \).

### Step 3: Set Up the Equations
Let the cost price (CP) of the article be \( x \).

1. Selling Price (SP) when sold at a gain of 12.5%:
\[ SP_1 = x + 0.125x = 1.125x \]

2. Selling Price (SP) when sold at a loss of \( \frac{50}{3} \% \):
\[ SP_2 = x - 0.1667x = 0.8333x \]

### Step 4: Set Up the Equation Based on the Given Information
According to the problem, the difference in selling prices when sold at gain and loss is Rs 1533:
\[ SP_1 - SP_2 = 1533 \]
Substituting the expressions for \( SP_1 \) and \( SP_2 \):
\[ 1.125x - 0.8333x = 1533 \]

### Step 5: Simplify the Equation
Combine like terms:
\[ (1.125 - 0.8333)x = 1533 \]
\[ 0.2917x = 1533 \]

### Step 6: Solve for the Cost Price (CP)
Now, divide both sides by 0.2917 to find \( x \):
\[ x = \frac{1533}{0.2917} \approx 5256 \]

### Conclusion
The cost price (CP) of the article is approximately Rs 5256.

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