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?

GATE 2024 AR — Planning – Question 8

General Aptitude · Quantitative Aptitude: Data Interpretation, Arithmetic and Number Computation · 2 marks · Multiple choice

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?

7.5%
10%
15%
20%

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Show answer and explanation

Correct answer: (B) 10%

Explanation

Let r be the annual return fraction of fund A. Person 1 earns ₹6000 from funds B and C, and ₹10000r from A. Person 2 earns ₹4500 from B and C, and ₹20000r from A. Their difference is therefore ₹(1500−10000r). Set this equal to ₹500: 10000r=1000, giving r=0.10. Thus A returns 10%, option B. Both invested ₹50000, so comparing final amounts gives the same difference as comparing their gains.

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