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GATE DA 2024 Q8: Rate of return of mutual fund A from two investors' totals

Question

Person 1 and Person 2 invest in three mutual funds A, B, and C. The amounts they invest in each of these mutual funds are given in the table.

Mutual fund AMutual fund BMutual fund C
Person 1₹10,000₹20,000₹20,000
Person 2₹20,000₹15,000₹15,000

At the end of one year, the total amount that Person 1 gets is ₹500 more than Person 2. The annual rate of return for the mutual funds B and C is 15% each. What is the annual rate of return for the mutual fund A?

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Answer: B (official GATE 2024 final answer key)

Concept used: Linear equation from simple returns on investments.

First step: Person 1 has ₹10,000 more in B+C at 15% and ₹10,000 less in A, so 10,000×1.15−10,000(1+r)=50010{,}000 \times 1.15 - 10{,}000(1+r) = 500.

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Source: official GATE 2024 DA question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key

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