A man purchased some eggs at 3 for Rs. 5 and sold them at 5 for Rs. 12. Thus he gained Rs. 143 in all. The number of eggs he bought is

Options

A. 210
B. 200
C. 195
D. 190

Answer

To solve the problem, we need to find out how many eggs the man bought based on the given cost price, selling price, and total profit.

### Step-by-Step Solution:

1. **Define Variables**:
Let the number of eggs purchased be \( X \).

2. **Calculate Cost Price**:
The cost price of 3 eggs is Rs. 5. Therefore, the cost price of 1 egg is:
\[ \text{Cost Price of 1 egg} = \frac{5}{3} \text{ Rs.} \]
Hence, the cost price of \( X \) eggs is:
\[ \text{Cost Price of } X \text{ eggs} = \frac{5}{3} X \text{ Rs.} \]

3. **Calculate Selling Price**:
The selling price of 5 eggs is Rs. 12. Therefore, the selling price of 1 egg is:
\[ \text{Selling Price of 1 egg} = \frac{12}{5} \text{ Rs.} \]
Hence, the selling price of \( X \) eggs is:
\[ \text{Selling Price of } X \text{ eggs} = \frac{12}{5} X \text{ Rs.} \]

4. **Set Up the Profit Equation**:
The profit is given as Rs. 143. Profit can be calculated as:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]
Therefore, we have:
\[ \frac{12}{5} X - \frac{5}{3} X = 143 \]

5. **Find a Common Denominator**:
The least common multiple (LCM) of 5 and 3 is 15. We will convert both fractions to have a common denominator of 15:
\[ \frac{12}{5} X = \frac{36}{15} X \quad \text{and} \quad \frac{5}{3} X = \frac{25}{15} X \]
So, the equation becomes:
\[ \frac{36}{15} X - \frac{25}{15} X = 143 \]

6. **Combine the Terms**:
Combine the fractions:
\[ \frac{36 - 25}{15} X = 143 \]
Simplifying gives:
\[ \frac{11}{15} X = 143 \]

7. **Solve for \( X \)**:
Multiply both sides by 15:
\[ 11X = 143 \times 15 \]
Now divide by 11:
\[ X = \frac{143 \times 15}{11} \]
Simplifying gives:
\[ X = 13 \times 15 = 195 \]

### Final Answer:
The number of eggs he bought is \( \boxed{195} \).