A sum of $12 million was divided between two investments. The smaller

Question

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A sum of $12 million was divided between two investments. The smaller portion was invested at 6%, and the remainder at 4%. The earnings from the 4% investment exceeded the earnings from the 6% investment by $20,000. Find the amount invested at each rate.

VivekSri · Answer

We can solve using below method

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pintukr · Answer

A sum of $12 million was divided between two investments. The smaller portion was invested at 6%, and the remainder at 4%. The earnings from the 4% investment exceeded the earnings from the 6% investment by $20,000. Find the amount invested at each rate.

Suppose,

smaller portion (@6%) = 100x
larger portion (@4%) = 100y

Putting all values in '000s, we get

100x + 100y = 12000
or, x + y = 120.....................(1)
-6x + 4y = 20................................(2)

Solving (1) & (2) equations, we get 
100x = 4600 ('000s) = 4.6 mn
100y = 7400 ('000s) = 7.4 mn

A. Amount invested at 6%

$4.6 million

B. Amount invested at 4%

$7.4 million

Gemmie · Answer

Small (S): 6%
Remainder (L): 4%

4%*L - 6%S = 20(k)

4L - 6S = 2 (million)
2L - 3S = 1
2L = 3S + 1

L + S = 12 
2L + 2S = 24
5S + 1 = 24
S =  \frac{23}{5} = 4.6

L = 12 - 4.6 = 7.4

Purnank · Answer

Lets assume x as a small investment therefore remaining amount is 12 - x
The smaller portion was invested at 6%, And larger portion is at 4%
Return on 4% - Return on 6% = 20k = 0.02 millions
(12-x)*4/100 - 6x/100 = 0.02
(48-4x - 6x) / 100 = 0.02
48-10x = 2
46 = 10x
x=4.6 mil
y=12 - 4.6 = 7.4 mil.

Gambrosio · Answer

we calculate: 12,000,000 * 0.04 = 480,000 and 12,000,000 * 0.06 = 720,000

now take the equation: 480,000 * x = 720,000 * (1-x) + 20,000 
solve for x: x = 7,400,000 which is the sum invested ate 4%.

The sum invested at 6% follows as 12,000,000 - 7,400,000 = 4,600,000

A sum of $12 million was divided between two investments. The smaller

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Amount invested at 6%	Amount invested at 4%
		$1.5 million
		$2.8 million
		$4.6 million
		$7.4 million
		$9.2 million
		$10.5 million

GMAT Two-part Analysis (TPA) Questions

A sum of $12 million was divided between two investments. The smaller

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