james and john invested ¥700 and ¥300 respectively, at the end the 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 james received ¥800 more than john did, what was the profit made by their business in that year?

To find the profit made by their business in that year, we need to follow the given information and set up equations based on the conditions provided.

Let's start by solving step by step:

1. Let's assume the total profit made by their business in that year is 'P'.

2. It is given that a third of the profit is divided equally for the efforts they have put into the business. This means that the remaining two-thirds of the profit is divided based on their investments.

3. James and John invested ¥700 and ¥300 respectively, so the ratio of their investments is 700:300, which simplifies to 7:3.

4. Let's assume the share for their efforts is 'E'. Therefore, the share for investments would be 2E (two-thirds of the profit).

5. Now, using the information given, we can set up the following equation:
7/10 * 2E - 3/10 * 2E = ¥800

Breaking it down:
James's share of investment (7/10 * 2E) - John's share of investment (3/10 * 2E) = ¥800

Simplifying the equation further:
14/10 * E - 6/10 * E = ¥800
8/10 * E = ¥800
E = ¥800 * 10/8
E = ¥1000

6. Now that we know the value of 'E', we can calculate the total profit (P):
P = 3/10 * E + 7/10 * 2E
= 3/10 * ¥1000 + 7/10 * ¥2000
= ¥300 + ¥1400
= ¥1700

Therefore, the profit made by their business in that year is ¥1700.