Mr Buffet and Mr Stark start a Robotics company by investing $14000 and $21000 respectively.Their agreement is to share half of their total profit equally and then share the remaining half in the ratio of their capitals. If they had shared the entire profit in the ratio of their capitals, Mr Stark would have got $ 1500 more than what he would have got otherwise.What is the total Profit?

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Mr. Buffet and Mr. Stark start a robotics company. Mr. Buffet invests fourteen thousand dollars, while Mr. Stark invests twenty-one thousand dollars. They agree to share half of their total profit equally between them, and then share the remaining half in the ratio of their capital investments. The key condition is that if they had shared the entire profit in the ratio of their capitals instead, Mr. Stark would have received fifteen hundred dollars more than under their current agreement. We need to find the total profit. Let's analyze the capital ratio first. Mr. Buffet invested fourteen thousand dollars and Mr. Stark invested twenty-one thousand dollars. To find their ratio, we divide both amounts by their greatest common divisor. Fourteen thousand to twenty-one thousand simplifies to fourteen to twenty-one, which further reduces to two to three. This means for every two parts that Mr. Buffet gets, Mr. Stark gets three parts. We have two different profit-sharing methods to compare: Method one is their current agreement where half the profit is shared equally and half is shared by capital ratio. Method two would be sharing the entire profit purely by the capital ratio of two to three. Now let's set up the mathematical equations. Let the total profit be P. Under Method 1, the current agreement, each person first gets P divided by 4 from the equal sharing of half the profit. Then from the remaining half, which is shared in the ratio 2 to 3, Buffet gets 2 parts out of 5, which is P divided by 5, while Stark gets 3 parts out of 5, which is 3P divided by 10. Under Method 2, the pure capital ratio method, Buffet would get 2 parts out of 5 of the total profit, and Stark would get 3 parts out of 5. The key equation comes from the condition that Stark gets 1500 dollars more under Method 2, so we set up: Stark's share in Method 2 minus Stark's share in Method 1 equals 1500. Let's solve the equation step by step. First, we calculate Stark's share under Method 1. P over 4 plus 3P over 10 equals 5P plus 6P over 20, which simplifies to 11P over 20. Next, Stark's share under Method 2 is 3P over 5, which equals 12P over 20. Now we set up our main equation: 12P over 20 minus 11P over 20 equals 1500. This simplifies to P over 20 equals 1500. Multiplying both sides by 20, we get P equals 30,000. Therefore, the total profit is thirty thousand dollars. Let's verify our answer of thirty thousand dollars. Under Method 1, the current agreement, each person gets 7,500 dollars from the equal sharing of half the profit. From the remaining 15,000 dollars shared by capital ratio, Buffet gets 6,000 dollars and Stark gets 9,000 dollars. This gives totals of 13,500 dollars for Buffet and 16,500 dollars for Stark. Under Method 2, the pure capital ratio method, Buffet would get 12,000 dollars and Stark would get 18,000 dollars. The difference for Stark is 18,000 minus 16,500, which equals 1,500 dollars, confirming our condition. Therefore, the total profit is thirty thousand dollars.