GATE 2024 CY – Question 8
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 A | Mutual fund B | Mutual 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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Correct answer: (B) 10%
Explanation
Let the annual return of fund A be $r$. Funds B and C return 15% each.
**Person 1** invests ₹10 000 in A and ₹20 000 + ₹20 000 = ₹40 000 in B and C:
$$\text{gain}_1=10\,000\,r+40\,000(0.15)=10\,000r+6000 .$$
**Person 2** invests ₹20 000 in A and ₹15 000 + ₹15 000 = ₹30 000 in B and C:
$$\text{gain}_2=20\,000\,r+30\,000(0.15)=20\,000r+4500 .$$
Both invest ₹50 000 in total, so Person 1 ends up with ₹500 more when
$$\text{gain}_1-\text{gain}_2=500 .$$
$$(10\,000r+6000)-(20\,000r+4500)=500\;\Rightarrow\;-10\,000r+1500=500\;\Rightarrow\;r=0.10 .$$
The rate of return of fund A is **10%** (option B).