Multiple choice

Mary and mike enter into a partnership by investing Rs. $700$ and Rs. $300$ 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 Rs. $800$ more than Mike did, what was the profit made by their business in that year?

  1. $1000$
  2. $2000$
  3. $3000$
  4. $4000$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ratio of investment = 700:300 = 7:3. Let total profit = P. 1/3 P is divided equally (P/6 each). 2/3 P is divided in 7:3 ratio (Mary gets 7/10 * 2/3 P = 7/15 P, Mike gets 3/10 * 2/3 P = 3/15 P = 1/5 P). Mary total = P/6 + 7/15 P = 19/30 P. Mike total = P/6 + 1/5 P = 11/30 P. Difference = 8/30 P = 800. P = 3000.

AI explanation

Let the total profit be P, meaning the remaining profit after setting aside a third for effort is 2P / 3. Since Mary and Mike invested in the ratio 700 : 300, or 7 : 3, Mary receives (7 / 10) of the remaining profit and Mike receives (3 / 10). The difference in their shares is (7 / 10 - 3 / 10) x (2P / 3) = 800, which simplifies to (4 / 10) x (2P / 3) = 800 and further to 4P / 15 = 800. Solving this gives P = 3000.

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