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14 Aug 2024, 07:42
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Exactly 3 investors—A, B, and C—invested in a certain business, each for a certain number of months. For these investments, what is the ratio of the profit earned by A to the profit earned by B to the profit earned by C ? (Note: Profit earned is proportional to the product of investment amount and investment duration.)
(1) A invested twice as much as B, and C invested half as much as A and B together.
(2) All 3 investments were for the same number of months.
ID: 700345
(1) A invested twice as much as B, and C invested half as much as A and B together.
(2) All 3 investments were for the same number of months.
ID: 700345
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14 Aug 2024, 08:02
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Exactly 3 investors—A, B, and C—invested in a certain business, each for a certain number of months. For these investments, what is the ratio of the profit earned by A to the profit earned by B to the profit earned by C ? (Note: Profit earned is proportional to the product of investment amount and investment duration.)
Let's say A, B, and C invested amounts $a, $b, and $c for x, y, and z months, respectively. The question asks for the ratio ax : by : cz.
(1) A invested twice as much as B, and C invested half as much as A and B together.
This implies a = 2b, and 2c = a + b. Substituting a = 2b into 2c = a + b gives 2c = 3b, which simplifies the ratio to 2bx : by : 3bz/2 = 2x : y : 3z/2. Since we know nothing about x, y, and z, this information alone is insufficient.
(2) All 3 investments were for the same number of months.
This implies x = y = z, which simplifies the ratio to ax : bx : cx = a : b : c. However, without knowing the amounts invested, this information alone is insufficient.
(1)+(2) Since from (2) x = y = z, from (1) the ratio becomes 2x : x : 3x/2 = 2 : 1 : 3/2. Sufficient.
Answer: C.
Let's say A, B, and C invested amounts $a, $b, and $c for x, y, and z months, respectively. The question asks for the ratio ax : by : cz.
(1) A invested twice as much as B, and C invested half as much as A and B together.
This implies a = 2b, and 2c = a + b. Substituting a = 2b into 2c = a + b gives 2c = 3b, which simplifies the ratio to 2bx : by : 3bz/2 = 2x : y : 3z/2. Since we know nothing about x, y, and z, this information alone is insufficient.
(2) All 3 investments were for the same number of months.
This implies x = y = z, which simplifies the ratio to ax : bx : cx = a : b : c. However, without knowing the amounts invested, this information alone is insufficient.
(1)+(2) Since from (2) x = y = z, from (1) the ratio becomes 2x : x : 3x/2 = 2 : 1 : 3/2. Sufficient.
Answer: C.
13 Mar 2025, 22:14
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What if the profit earned was 0? The question stem is saying that profit is proporational to months and investment, but who is there to say that someone actually made money? Ie. the profit equation could be: Dividend Yield * (Total investment) = Dividend Yield * Months Invested * Invested per month. What if the dividend yield was 0 this year?
