Sam bought an article at Rs.14800. He marks up the cost of article and sells it in such a way that if he will give `46(2)/(3)%` discount, then loss occur to him is equal to profit earned by him when he will give 30% discount. Find the mark price of article.

Options

A. Rs. 24000
B. Rs. 30000
C. Rs. 25000
D. Rs. 27000

Answer

To solve the problem, we will denote the marked price of the article as \( M \).

1. **Understanding the Cost Price and Selling Price**:
- The cost price (CP) of the article is given as Rs. 14,800.
- The selling price (SP) after giving a discount can be calculated using the formula:
\[ SP = M - \text{Discount} \]

2. **Calculating Selling Price with 46(2/3)% Discount**:
- The discount of \( 46(2/3)\% \) can be converted to a fraction:
\[ 46(2/3)\% = \frac{140}{3}\% = \frac{140}{3 \times 100} = \frac{14}{30} = \frac{7}{15} \]
- Therefore, the selling price with this discount is:
\[ SP_1 = M - \left( \frac{7}{15}M \right) = \frac{8}{15}M \]

3. **Calculating Selling Price with 30% Discount**:
- The selling price with a 30% discount is:
\[ SP_2 = M - 0.30M = 0.70M \]

4. **Loss and Profit Relationship**:
- According to the problem, the loss incurred when giving a \( 46(2/3)\% \) discount is equal to the profit earned when giving a 30% discount.
- Loss when selling at \( SP_1 \):
\[ \text{Loss} = CP - SP_1 = 14800 - \frac{8}{15}M \]
- Profit when selling at \( SP_2 \):
\[ \text{Profit} = SP_2 - CP = 0.70M - 14800 \]

5. **Setting Up the Equation**:
- Since the loss equals the profit:
\[ 14800 - \frac{8}{15}M = 0.70M - 14800 \]

6. **Solving the Equation**:
- Rearranging the equation:
\[ 14800 + 14800 = 0.70M + \frac{8}{15}M \]
\[ 29600 = 0.70M + \frac{8}{15}M \]
- Converting \( 0.70M \) to a fraction:
\[ 0.70M = \frac{7}{10}M \]
- Finding a common denominator (30):
\[ \frac{7}{10}M = \frac{21}{30}M \]
- Now, we can combine the fractions:
\[ 29600 = \left( \frac{21}{30} + \frac{16}{30} \right)M = \frac{37}{30}M \]
- Multiplying both sides by \( \frac{30}{37} \):
\[ M = \frac{29600 \times 30}{37} \]
- Calculating \( M \):
\[ M = \frac{888000}{37} \approx 24000 \]

7. **Final Answer**:
- The marked price of the article is approximately Rs. 24,000.