Split investment to equalize dividend income Rs. 2780 is invested partly in 4% stock at 75 and partly in 5% stock at 80 so that the two incomes are equal. How much is invested in the 5% stock?

Introduction / Context:
When different stocks are bought at different prices and rates, equalizing income requires matching the product of (investment/price) and dividend%. This problem asks how to split a fixed total investment between two such stocks to get the same rupee dividend from each part.

Given Data / Assumptions:

• Total investment = Rs. 2780.
• Stock A: 4% at 75.
• Stock B: 5% at 80.
• Brokerage and taxes are neglected.

Concept / Approach:
Income(A) = (Investment_A / 75) * 4. Income(B) = (Investment_B / 80) * 5. Set Income(A) = Income(B) and use Investment_A + Investment_B = 2780. Solve for Investment_B (the 5% portion).

Step-by-Step Solution:
Let x = investment in 4% stock. Then (2780 − x) is in 5% stock.Equal incomes: (x/75)*4 = ((2780 − x)/80)*5.Multiply through: 4x/75 = 5(2780 − x)/80 ⇒ 320x = 375(2780 − x).320x = 375*2780 − 375x ⇒ 695x = 375*2780.x = (375*2780)/695 = 1500 ⇒ investment in 5% stock = 2780 − 1500 = Rs. 1280.

Verification / Alternative check:
Compute incomes: From 4% part: (1500/75)*4 = 20*4 = 80. From 5% part: (1280/80)*5 = 16*5 = 80. Incomes match as required.

Why Other Options Are Wrong:
Rs. 1500 is the 4% portion, not the 5% portion; Rs. 1434.84 and Rs. 1640 result from algebra or arithmetic slips; Rs. 1225 does not balance incomes.

Common Pitfalls:
Equating investments instead of incomes, or forgetting to divide by quoted price before multiplying by the dividend rate. Always convert investment to the number of Rs. 100 nominal units first (via price), then apply the percentage.

Final Answer:
Rs. 1280