Equal dividend condition between two quoted stocks A man invests some money partly in 3% stock at 96 and partly in 4% stock at 120. To receive equal dividend from both parts, in what ratio should the investments be made (3% : 4%)?

Introduction / Context:
To equalize dividend from two stocks purchased at different quotations and coupon rates, the investment amounts must be inversely proportional to dividend-per-rupee-invested for each stock. This yields a solvable ratio relation.

Given Data / Assumptions:

• Stock A: 3% at 96.
• Stock B: 4% at 120.
• We want Income(A) = Income(B).

Concept / Approach:
If x is invested in A and y in B, then Income(A) = (x/96)*3 and Income(B) = (y/120)*4. Set them equal and derive x:y.

Step-by-Step Solution:
(x/96)*3 = (y/120)*4.3x/96 = 4y/120 ⇒ x/32 = y/30.Therefore x : y = 32 : 30 = 16 : 15.

Verification / Alternative check:
Test with numbers: Invest Rs. 16,000 in A ⇒ Income = (16000/96)*3 = 166.667*3 ≈ 500. Invest Rs. 15,000 in B ⇒ Income = (15000/120)*4 = 125*4 = 500. Equal incomes confirm the ratio.

Why Other Options Are Wrong:
3:4, 4:5, and 3:5 ignore the price effect; 20:19 is arbitrary and does not satisfy the income equality.

Common Pitfalls:
Equating rupee investments instead of rupee incomes, or forgetting to divide by quoted price before applying the percentage dividend.

Final Answer:
16 : 15