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Tom invested part of $8,000 at 3 percent and the rest at 5 percent a

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Tom invested part of $8,000 at 3 percent and the rest at 5 percent a [#permalink] New post   12 Feb 2021, 06:26
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Tom invested part of $8,000 at 3 percent and the rest at 5 percent annual interest for a total return of $340.

Quantity A
Quantity B
The amount invested at 3%
The amount invested at 5%



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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B
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Tom invested part of $8,000 at 3 percent and the rest at 5 percent a [#permalink] New post   12 Feb 2021, 08:26
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Total $8000

Let's say $x is invested at 3% & $(8000-x) is invested at 5%

Interest = 340 = \(\frac{x * 3 * 1}{100}\) + \(\frac{(8000-x) * 5 * 1}{100}\)

340 = \(\frac{3x}{100}\) + \(\frac{40000 - 5x}{100}\)

340 = 400 - \(\frac{2x}{100}\)

2x = 6000

\(x = 3000\)

Qt A = 3000

Qt B = 5000

Qt B > Qt A

Answer B
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Re: Tom invested part of $8,000 at 3 percent and the rest at 5 percent a [#permalink] New post   12 Feb 2021, 20:11
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x + y = 8000
3/100x +5/100y = 340

Solve for x & y

x = 3000; y = 5000
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Re: Tom invested part of $8,000 at 3 percent and the rest at 5 percent a [#permalink] New post   13 Feb 2021, 11:02
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If the entire $8000 were invested at 3% the return would be $240 and if it were invested at 5% the return would be $400. Since the actual return of $340 is closer to $400 than $240, a greater proportion of the money must have been invested at 5%. Thus the correct answer is (B).
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Re: Tom invested part of $8,000 at 3 percent and the rest at 5 percent a [#permalink] New post   12 Jul 2024, 00:02
Question did not mention whether its compound or simple interest. So I thought Relation cannot be determined would be the answer. Those are the only 2 possibilities.
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Re: Tom invested part of $8,000 at 3 percent and the rest at 5 percent a [#permalink] New post   12 Jul 2024, 00:23
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In this case the interest is uniform.

There is nothing that suggests us it is compounded.

It reasonable to think that it is simple.

However, I reckon that could be there the benefit of doubt
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Re: Tom invested part of $8,000 at 3 percent and the rest at 5 percent a [#permalink]
12 Jul 2024, 00:23
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