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Mary and Mike enter into a partnership by investing $700 and

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Mary and Mike enter into a partnership by investing $700 and  [#permalink]

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New post 22 Aug 2013, 11:46
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Mary and Mike enter into a partnership by investing $700 and $300 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $800 more than Mike did, what was the profit made by their business in that year?

A. $2000
B. $6000
C. $4000
D. $1333
E. $3000

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Re: Mary and Mike enter into a partnership by investing $700 and  [#permalink]

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New post 22 Aug 2013, 11:54
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Asifpirlo wrote:
Mary and Mike enter into a partnership by investing $700 and $300 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $800 more than Mike did, what was the profit made by their business in that year?

A. $2000
B. $6000
C. $4000
D. $1333
E. $3000


Say the profit was $x.

Mary's share = x/6 (half of the third) + (x-x/3)*0.7
Mike's share = x/6 (half of the third) + (x-x/3)*0.3

Thus (x-x/3)*0.7-(x-x/3)*0.3=800 --> x=3000.

Answer: D.
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Re: Mary and Mike enter into a partnership by investing $700 and  [#permalink]

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New post 22 Aug 2013, 19:15
they divided 2/3rd amount in 7:3 ratio and 1/3 amount as 1:1 ratio.
We can observe that the $800 excess that mary got is from 2/3rd amount, because they shared 1/3rd in 1:1 ratio.

so different in 2/3rd amount -> 7x-3x = 800 => x = 200
total amount shared in 7:3 ratio is 10x = 200*10 => 2000

now 2/3rd amount = 2000 = > amount = 3000
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Re: Mary and Mike enter into a partnership by investing $700 and  [#permalink]

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New post 19 Oct 2017, 10:23
Asifpirlo wrote:
Mary and Mike enter into a partnership by investing $700 and $300 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $800 more than Mike did, what was the profit made by their business in that year?

A. $2000
B. $6000
C. $4000
D. $1333
E. $3000


Since Mary and Mike invest $700 and $300, respectively, into the partnership, they will get 7/10 and 3/10 of the profit, respectively, after ⅓ of the profit is divided equally. In other words, Mary will get 7/10 and Mike will get 3/10 of the remaining ⅔ of the profit.

If we let x = the amount of profit in dollars, then Mary gets (½)(⅓)(x) + (7/10)(⅔)(x) = x/6 + 7x/15 dollars and Mike gets (½)(⅓)(x) + (3/10)(⅔)(x) = x/6 + x/5 dollars.

Since Mary gets $800 more than Mike, we have the following equation:

x/6 + 7x/15 = x/6 + x/5 + 800

7x/15 = x/5 + 800

Multiplying both sides by 15, we have:

7x = 3x + 12,000

4x = 12,000

x = 3,000

Answer: E
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Re: Mary and Mike enter into a partnership by investing $700 and  [#permalink]

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New post 19 Oct 2017, 10:39
So they have divided 1/3 of profit amount equally. Rest 2/3 of the amount is to be split in the ratio 7:3. So Mary gets 70% and Mike gets 30%. This creates a difference of 40%, which in turn is given to be $800

So 40% of 2/3 of total amount = $800
So total amount = (800*3)/(2*0.4) = $3000

Hence E answer
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Re: Mary and Mike enter into a partnership by investing $700 and  [#permalink]

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New post 07 Jan 2018, 03:00
Asifpirlo wrote:
Mary and Mike enter into a partnership by investing $700 and $300 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $800 more than Mike did, what was the profit made by their business in that year?

A. $2000
B. $6000
C. $4000
D. $1333
E. $3000



Let Mike's Profit = x, then Mary's Profit = x + 800

The remaining of the total profit (2/3 of the profit) is distributed the same as their ratios in investment.

\(\frac{x}{x+ 800}\) = \(\frac{300}{700}\)

Solve for x, we get x =600

2/3 of the total profit =2000

Total profit = 3000
Answer: E
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Re: Mary and Mike enter into a partnership by investing $700 and &nbs [#permalink] 07 Jan 2018, 03:00
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