A man sells Rs. 5,000 nominal of 12% stock at Rs. 156 and receives Rs. 7,800. He reinvests the proceeds partly in 8% stock at Rs. 90 and partly in 9% stock at Rs. 108, thereby increasing his annual income by Rs. 70. How much of the proceeds are invested in each stock?

Introduction / Context:
This is a classic stocks and shares word problem involving sale of an existing investment and reinvestment of the proceeds into two different stocks. The key challenge is to relate the original dividend income and the new dividend income so that we can determine how the proceeds were split between the two new stocks. The question combines concepts of nominal value, market value, and dividend yield.

Given Data / Assumptions:

• Original holding: Rs. 5,000 nominal of 12% stock.
• Selling price of original stock = Rs. 156 per Rs. 100 nominal.
• Proceeds from sale = 5000 * 156 / 100 = Rs. 7,800.
• New stocks: 8% stock at Rs. 90 and 9% stock at Rs. 108.
• Increase in annual income after reinvestment = Rs. 70.
• No brokerage is mentioned, so it is ignored.

Concept / Approach:
First find the original annual income from the 12% stock. Then express the new income from the two investments in terms of the unknown amounts invested in the 8% and 9% stocks. Setting new income equal to old income plus Rs. 70 gives a linear equation that can be solved for one of the investment amounts. The remainder of the proceeds is invested in the other stock.

Step-by-Step Solution:
Step 1: Original income from 12% stock = 12% of Rs. 5,000 nominal = (12 / 100) * 5000 = Rs. 600. Step 2: Total sale proceeds = 5000 * 156 / 100 = Rs. 7,800. Step 3: Let x rupees be invested in 8% stock at Rs. 90. Then income from this part = (x / 90) * 8. Step 4: Remaining amount invested in 9% stock = 7800 - x. Income from this part = ((7800 - x) / 108) * 9. Step 5: Total new income = (x / 90) * 8 + ((7800 - x) / 108) * 9. Step 6: New income is greater than old income by Rs. 70, so: (x / 90) * 8 + ((7800 - x) / 108) * 9 = 600 + 70 = 670. Step 7: Simplify each term: (8x / 90) = (4x / 45) and (9(7800 - x) / 108) = (7800 - x) / 12. Step 8: So the equation becomes 4x / 45 + (7800 - x) / 12 = 670. Step 9: Solve this equation to get x = Rs. 3,600. Step 10: Therefore, investment in 8% stock = Rs. 3,600 and investment in 9% stock = 7,800 - 3,600 = Rs. 4,200.

Verification / Alternative check:
Income from Rs. 3,600 in 8% stock at Rs. 90: nominal value = (3600 / 90) * 100 = Rs. 4,000, income = 8% of 4,000 = Rs. 320. Income from Rs. 4,200 in 9% stock at Rs. 108: nominal value = (4200 / 108) * 100 = Rs. 3,888.89 approximately, income ≈ 9% of 3,888.89 ≈ Rs. 350. New total income ≈ 320 + 350 = Rs. 670, which is Rs. 70 more than the original Rs. 600.

Why Other Options Are Wrong:
Exchanging the two amounts (as in option B) changes the nominal values and gives a different income. The other splits such as (4,000, 3,800) or (5,000, 2,800) do not satisfy the required increase of Rs. 70 in total income when proper yield calculations are performed. Only Rs. 3,600 in 8% stock and Rs. 4,200 in 9% stock produce the correct increment.

Common Pitfalls:
Students may incorrectly assume that income is directly proportional to money invested without adjusting for different market prices. Another mistake is to use the percentage on the invested amount instead of on the nominal value. Careful formulation of income expressions for each stock is critical to solving such problems correctly.

Final Answer:
The man invests Rs. 3,600 in 8% stock and Rs. 4,200 in 9% stock.