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A business allocates $7.2 million between two investments. It invests 10 Oct 2023, 10:21
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Rate of return on real estate: 13.5%
Rate of return on currencies: 7.5%
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Data Insights (DI) Butler 2023-24 [Question #23, Date: Oct-09-2023] [Click here for Details]

A business allocates $7.2 million between two investments. It invests the smaller portion in currencies and the remainder in real estate. The combined return on the investments for the first year is $846,000. If the investment in real estate exceeds the currency investment by $3 million, find the rate of return on each investment.

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Rate of return on real estate Rate of return on currencies
2.2%
3.8%
7.5%
9.1%
11.75%
13.5%
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Rate of return on real estate: 13.5%
Rate of return on currencies: 7.5%
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A business allocates $7.2 million between two investments. It invests 11 Oct 2023, 05:46
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11.75
11.75
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A business allocates $7.2 million between two investments. It invests 12 Oct 2023, 06:20
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Can someone please share the solution for this?
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A business allocates $7.2 million between two investments. It invests 12 Oct 2023, 23:08
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Official Explanation

Because the total of the two investments and the difference between them are both known, it is possible to determine that the smaller investment (x) is $2.1 million and the larger (x + $3 million) is $5.1 million: x + x + $3 million = $7.2 million, so 2x = $4.2 million, and x = $2.1 million.

The combined return is 11.75% of the total amount, suggesting that the interest rates are among the higher choices, so begin by finding 13.5% of $5.1 million = $688,500. Subtract that from the total return of $846,000 to get $157,500. Divide $157,500 by $2.1 million to find that the second interest rate was 7.5%.
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A business allocates $7.2 million between two investments. It invests 18 Oct 2023, 03:12
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Official Explanation

Because the total of the two investments and the difference between them are both known, it is possible to determine that the smaller investment (x) is $2.1 million and the larger (x + $3 million) is $5.1 million: x + x + $3 million = $7.2 million, so 2x = $4.2 million, and x = $2.1 million.

The combined return is 11.75% of the total amount, suggesting that the interest rates are among the higher choices, so begin by finding 13.5% of $5.1 million = $688,500. Subtract that from the total return of $846,000 to get $157,500. Divide $157,500 by $2.1 million to find that the second interest rate was 7.5%.
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Hi, why can't both investment provide returns of 11.75%? Its not mentioned in the question stem that interest rate for both investments have to be different.
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A business allocates $7.2 million between two investments. It invests 21 Oct 2023, 08:30
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Sajjad1994
Official Explanation

Because the total of the two investments and the difference between them are both known, it is possible to determine that the smaller investment (x) is $2.1 million and the larger (x + $3 million) is $5.1 million: x + x + $3 million = $7.2 million, so 2x = $4.2 million, and x = $2.1 million.

The combined return is 11.75% of the total amount, suggesting that the interest rates are among the higher choices, so begin by finding 13.5% of $5.1 million = $688,500. Subtract that from the total return of $846,000 to get $157,500. Divide $157,500 by $2.1 million to find that the second interest rate was 7.5%.
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There's no mention of allocation for the Currency and Real Estate is done with equal weightage. So, why 2x comes here in the equation? Sajjad1994 bb Bunuel or any other person / expert?
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A business allocates $7.2 million between two investments. It invests 22 Oct 2023, 03:18
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Sajjad1994
Official Explanation

Because the total of the two investments and the difference between them are both known, it is possible to determine that the smaller investment (x) is $2.1 million and the larger (x + $3 million) is $5.1 million: x + x + $3 million = $7.2 million, so 2x = $4.2 million, and x = $2.1 million.

The combined return is 11.75% of the total amount, suggesting that the interest rates are among the higher choices, so begin by finding 13.5% of $5.1 million = $688,500. Subtract that from the total return of $846,000 to get $157,500. Divide $157,500 by $2.1 million to find that the second interest rate was 7.5%.

There's no mention of allocation for the Currency and Real Estate is done with equal weightage. So, why 2x comes here in the equation? Sajjad1994 bb Bunuel or any other person / expert?
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x = investment 1

as we know, the second investment is 3 million greater than first investment hence second investment would equal to x + 3 million and sum of both investment would equal to x + x + 3 million and x + x + 3 million = 2x+ 3 million.
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A business allocates $7.2 million between two investments. It invests 22 Oct 2023, 03:20
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Official Explanation

Because the total of the two investments and the difference between them are both known, it is possible to determine that the smaller investment (x) is $2.1 million and the larger (x + $3 million) is $5.1 million: x + x + $3 million = $7.2 million, so 2x = $4.2 million, and x = $2.1 million.

The combined return is 11.75% of the total amount, suggesting that the interest rates are among the higher choices, so begin by finding 13.5% of $5.1 million = $688,500. Subtract that from the total return of $846,000 to get $157,500. Divide $157,500 by $2.1 million to find that the second interest rate was 7.5%.

Hi, why can't both investment provide returns of 11.75%? Its not mentioned in the question stem that interest rate for both investments have to be different.
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The official explanation is correct, but the language of the question is ambigious, so bear it as it is.
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A business allocates $7.2 million between two investments. It invests 15 Dec 2023, 09:26
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Sajjad1994 bb Bunuel - why can't both be 11.75 .
11.75 % return on each investment gives 846,000 as the total return.
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A business allocates $7.2 million between two investments. It invests 16 Dec 2023, 13:25
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Parvez786
Sajjad1994 bb Bunuel - why can't both be 11.75 .
11.75 % return on each investment gives 846,000 as the total return.
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Because the statement of the question was said as such. Read the last line of the question. Also, read the OE.

Thank you!
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A business allocates $7.2 million between two investments. It invests 23 Dec 2024, 16:34
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