A cooperative decided to distribute \( 15 \% \) dividend of the net profit cams in the year. It had distributed 12000 shares. a. The cooperative carmed net proff of Rs. \( 22,00,000 \) in a year. Wh dividend does a person with 250 shares receive? b. What should be the net profit of the cooperative so that each share shot receive Rs. 35 at same tate of dividend"

To solve the problem, we will first calculate the dividend per share based on the given net profit and then determine the required net profit for a specific dividend per share. ### Part (a) 1. **Calculate the total dividend distributed:** The cooperative decided to distribute \( 15\% \) of the net profit. The net profit is Rs. \( 22,00,000 \). \[ \text{Total Dividend} = 15\% \text{ of } 22,00,000 = \frac{15}{100} \times 22,00,000 = 3,30,000 \] 2. **Calculate the dividend per share:** The total number of shares is \( 12,000 \). \[ \text{Dividend per share} = \frac{\text{Total Dividend}}{\text{Total Shares}} = \frac{3,30,000}{12,000} = 27.5 \] 3. **Calculate the dividend for a person with 250 shares:** \[ \text{Dividend for 250 shares} = 250 \times 27.5 = 6,875 \] So, a person with 250 shares receives Rs. \( 6,875 \). ### Part (b) 1. **Determine the required net profit for each share to receive Rs. 35:** We want each share to receive Rs. \( 35 \). Let \( x \) be the required net profit. The total dividend distributed will still be \( 15\% \) of \( x \). \[ \text{Total Dividend} = 15\% \text{ of } x = \frac{15}{100} \times x = 0.15x \] 2. **Calculate the total dividend based on the number of shares:** The total dividend can also be expressed in terms of the dividend per share and the total number of shares: \[ \text{Total Dividend} = \text{Dividend per share} \times \text{Total Shares} = 35 \times 12,000 = 4,20,000 \] 3. **Set the two expressions for total dividend equal to each other:** \[ 0.15x = 4,20,000 \] 4. **Solve for \( x \):** \[ x = \frac{4,20,000}{0.15} = 28,00,000 \] So, the net profit of the cooperative should be Rs. \( 28,00,000 \) so that each share receives Rs. \( 35 \) at the same rate of dividend.