Company Value Calculation from Share Sale

This problem involves calculating the total value of a company based on the sale of a portion of shares by a specific shareholder.

Understanding the Problem

We are given the following information:

• Rakesh owns a fraction of $ \frac{2}{15} $ of the company's shares.
• He sells $ \frac{1}{3} $ of the shares he owns.
• The selling price for this portion was Rs. $ 75,000 $.
• We need to find the total value of the company.

Step 1: Calculate the Fraction of Total Shares Sold

First, let's determine what fraction of the total company shares Rakesh sold. He sold $ \frac{1}{3} $ of his own shares, and he owned $ \frac{2}{15} $ of the total shares.

Fraction of total shares sold = (Fraction of Rakesh's shares sold) $ \times $ (Fraction of company owned by Rakesh)

Fraction of total shares sold = $ \frac{1}{3} \times \frac{2}{15} $

To multiply these fractions, we multiply the numerators together and the denominators together:

Fraction of total shares sold = $ \frac{1 \times 2}{3 \times 15} = \frac{2}{45} $

So, Rakesh sold $ \frac{2}{45} $ of the total shares of the company.

Step 2: Relate Sold Shares Value to Total Company Value

We know that the fraction $ \frac{2}{45} $ of the company's shares was sold for Rs. $ 75,000 $. This means that this amount represents the value of $ \frac{2}{45} $ of the company.

Let the total value of the company be represented by $ V $.

Therefore, we can write the equation:

$ \frac{2}{45} \times V = 75,000 $

Step 3: Calculate the Total Value of the Company

To find the total value $ V $, we need to rearrange the equation:

$ V = 75,000 \div \frac{2}{45} $

Dividing by a fraction is the same as multiplying by its reciprocal:

$ V = 75,000 \times \frac{45}{2} $

Now, we perform the calculation:

$ V = \frac{75,000 \times 45}{2} $

$ V = \frac{3,375,000}{2} $

$ V = 1,687,500 $

The total value of the company is Rs. $ 1,687,500 $.

Conclusion

By calculating the fraction of total shares Rakesh sold and equating it to the sale price, we determined the total market value of the company.