Rs. 9800 is split between a 9% stock at 75 and a 10% stock at 80 to yield equal incomes. What is the amount invested in the 9% stock___________?
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Answer: C. Rs. 5000
Explanation
Letting the investment in the first stock be x allows expressing the second stock investment as ninety-eight hundred minus x. Equating the annual incomes generated by both stock investments forms a solvable algebraic proportion. Solving this income equality equation reveals that exactly five thousand rupees was invested in the first stock. Stock income equals the nominal dividend multiplied by the number of shares purchased at market price. Splitting a total investment sum requires ensuring the sum of both parts equals the original capital amount. Equating investment returns is a standard technique for balancing income streams in financial mathematics.
Investors compare different dividend yields to allocate capital across equities for balanced income generation. Financial advisors use proportion equations to structure diversified portfolios meeting specific income goals. Solving stock allocation problems reinforces linear equation setup and fraction simplification skills. Option A underestimates the capital allocated to the first stock, yielding unequal income totals. Option B overshoots the required investment balance, violating the income equality condition. Option D allocates too much capital to the first stock, causing its generated income to exceed the second.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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