The problem states that three partners invested a total of Php 960,000, with each investing different percentages of the total (25%, 35%, and 40%). The partner with the smallest investment (25%) received a profit of Php 90,000. We need to calculate the profit received by the largest investor (40%).

Let's proceed step by step:

Step 1: Determine the ratio of investments.

• First partner (25%): $\frac{25}{100} \times 960,000 = 240,000$
• Second partner (35%): $\frac{35}{100} \times 960,000 = 336,000$
• Third partner (40%): $\frac{40}{100} \times 960,000 = 384,000$

The profits are divided according to the investment proportions.

Step 2: Set up a proportion for profit distribution.

• The smallest investor received Php 90,000. The ratio of the profits is the same as the ratio of their investments.
• Let $P_1$, $P_2$, and $P_3$ be the profits for the first, second, and third investors respectively. Using the same ratio of investments, we have:

$\frac{P_1}{240,000} = \frac{P_2}{336,000} = \frac{P_3}{384,000}$

Given that $P_1 = 90,000$, the ratio for the smallest investor is:

$\frac{90,000}{240,000} = \frac{3}{8}$

Step 3: Calculate the profit for the largest investor.

Using the same ratio, the profit for the largest investor is:

$P_3 = \frac{3}{8} \times 384,000 = 144,000$

Final Answer:

The largest investor received a profit of Php 144,000.

Do you want more details or have any other questions?

Here are some follow-up questions for better understanding:

1. How is the profit-sharing ratio determined in investment situations?
2. What are the other possible ways profits can be divided among investors?
3. If the total profit had been distributed equally, how much would each partner receive?
4. How would the profit distribution change if one partner withdrew part of their investment?
5. What would happen if the business made a loss instead of a profit?

Tip: Always check the proportionality in investment-related problems to ensure the division of profits is fair based on the input.