1. **Problem statement:** A man invests equally in shares of two companies A and B. Company A's shares are priced at a 20% premium on 100 rupees and pay an 8% dividend. Company B's shares are priced at a 10% discount on 100 rupees and pay a 7% dividend. The total dividend income is 936. We need to find the total amount invested. 2. **Understanding the problem:** - Face value of each share = 100 rupees. - Price of A's share = 100 + 20% of 100 = 100 + 20 = 120 rupees. - Price of B's share = 100 - 10% of 100 = 100 - 10 = 90 rupees. - Dividend rate for A = 8% of face value = 8 rupees per share. - Dividend rate for B = 7% of face value = 7 rupees per share. 3. **Let the amount invested in each company be $x$ rupees.** 4. **Number of shares bought:** - Shares of A = $\frac{x}{120}$ - Shares of B = $\frac{x}{90}$ 5. **Dividend from each company:** - Dividend from A = number of shares $\times$ dividend per share = $\frac{x}{120} \times 8 = \frac{8x}{120} = \frac{2x}{30}$ - Dividend from B = $\frac{x}{90} \times 7 = \frac{7x}{90}$ 6. **Total dividend = 936:** $$\frac{2x}{30} + \frac{7x}{90} = 936$$ 7. **Find common denominator and solve:** - Common denominator = 90 - Rewrite: $$\frac{2x}{30} = \frac{2x \times 3}{30 \times 3} = \frac{6x}{90}$$ - So, $$\frac{6x}{90} + \frac{7x}{90} = \frac{13x}{90} = 936$$ 8. **Solve for $x$:** $$13x = 936 \times 90$$ $$13x = 84240$$ $$x = \frac{84240}{13} = 6480$$ 9. **Total investment:** Since the man invests equally in both companies, total investment = $x + x = 2x = 2 \times 6480 = 12960$ rupees. **Final answer:** The man invested a total of 12960 rupees.