A man invests some money partly in 9% stock at Rs. 96 and partly in 12% stock at Rs. 120, and he receives equal dividends from both. In what ratio must he invest in the two stocks to make the dividends equal?

Introduction / Context:
This question is about dividing an investment between two different stocks such that the dividend income from each stock is the same. The two stocks have different dividend rates and different market prices, so the amount invested in each must be carefully chosen to equalise the annual income from them.

Given Data / Assumptions:

• First stock: 9% stock at Rs. 96 per Rs. 100 nominal.
• Second stock: 12% stock at Rs. 120 per Rs. 100 nominal.
• Dividend is calculated on nominal value, while investment is made at the market price.
• Dividends received from both investments must be equal.

Concept / Approach:
Let the money invested in the 9% stock be x rupees and the money invested in the 12% stock be y rupees. We compute the dividend from each in terms of x and y, then set these dividends equal. This yields an equation that gives the ratio x : y. Income from each stock is found by converting investment to nominal value and then applying the dividend rate.

Step-by-Step Solution:
Step 1: For the 9% stock at Rs. 96, nominal value bought with x rupees = (x / 96) * 100. Step 2: Dividend from this nominal value at 9% = 9% of (x / 96 * 100) = (9 / 100) * (x / 96 * 100) = 9x / 96. Step 3: For the 12% stock at Rs. 120, nominal value bought with y rupees = (y / 120) * 100. Step 4: Dividend from this nominal value at 12% = 12% of (y / 120 * 100) = 12y / 120 = y / 10. Step 5: We are told that dividends from both investments are equal, so: 9x / 96 = y / 10. Step 6: Cross multiply: 9x * 10 = 96y, so 90x = 96y. Step 7: Divide both sides by 6 to simplify: 15x = 16y. Step 8: Therefore, x / y = 16 / 15, so the required investment ratio is 16 : 15.

Verification / Alternative check:
Assume we invest 16,000 rupees in the 9% stock and 15,000 rupees in the 12% stock. The nominal value for the first stock is (16000 / 96) * 100 ≈ 16,666.67, giving dividend ≈ 0.09 * 16666.67 ≈ 1,500. For the second stock, nominal value = (15000 / 120) * 100 = 12,500, dividend = 0.12 * 12500 = 1,500. The dividends are equal, confirming the ratio 16 : 15.

Why Other Options Are Wrong:
Ratios such as 3 : 5, 2 : 1, 4 : 5, or 5 : 4 do not produce equal dividends when used as x : y in the calculations above. Only 16 : 15 ensures that the dividend from the 9% stock matches the dividend from the 12% stock for any common multiple of investments.

Common Pitfalls:
A typical mistake is to compare only the percentages 9% and 12% and ignore the differing market prices. Some learners also incorrectly take the ratio of dividend rates to decide the investment split. The correct method is to equate the actual dividend amounts derived from the investments, which involves both dividend rates and market prices.

Final Answer:
To obtain equal dividends from both stocks, the investor must invest in the ratio 16 : 15 in 9% stock at Rs. 96 and 12% stock at Rs. 120.