let x= profit

2/3x is profit split based on level of contribution
mary contributes 7/10 of investment
mike contributes 3/10 of investment

mary: (2/3)(7/10)x
mike: (2/3)(3/10)x

mike+800=mary

6x/30+800=14x/30

x=3000 profit

Profit = 30 x
1/3 = 10x so share of Mary and Mike = 5x each
Investement Ratio of Mary : Mike = 7 : 3 so 20x is divided in 14x : 6x
Mary - Mike = 19x- 11x = 800

IMO E

Lets x be the profit.

X/3 is divided equally.

So each will get x/6

remaining 2x/3 to be divided with ratio7:3


-->Mary ratio 7x/15 and mike ratio 3x/15


Adding,

x/6+7x/15=x/6+3x/15+800

x=3000

diff in profit will come for the 2/3 which marry :mike will divide in the ratio of 7:3 ..so merry will get 4 /10 extra than mike

now (4/10 )*(2/3) of profit=800

or profit =3000
Ans option D

gmatmachoman 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 1/3 of the profit is divided equally. In other words, Mary will get 7/10 and Mike will get 3/10 of the remaining 2/3 of the profit.

If we let x = the amount of profit in dollars, then Mary gets (1/2)(1/3)(x) + (7/10)(2/3)(x) = x/6 + 7x/15 dollars and Mike gets (1/2)(1/3)(x) + (3/10)(2/3)(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

gmatmachoman 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 1/3 of the total profit is divided equally, the $800 difference between Mary's and Mike's earnings is yielded by 2/3 of the total profit.
This $800 difference must be in the same ratio as the two investments:
700:300 = 1400:600.
The values in blue yield the required $800 difference, implying that 2/3 of the total profit = 1400+600 = 2000.
Thus, 2/3 of the correct answer choice must be equal to $2000.
Only E works:
(2/3)(3000) = 2000.

The correct answer is E.