To divide the profit of $1920 in proportion to the amounts invested, we first need to determine the ratio of each man’s investment to the total investment.

Step 1: Calculate the total investment

The total investment is the sum of the three individual investments: $2000 + 3000 + 5000 = 10000$

Step 2: Find the ratio of each person's investment

• The man who invested $2000:
  $\frac{2000}{10000} = 0.2$
• The man who invested $3000:
  $\frac{3000}{10000} = 0.3$
• The man who invested $5000:
  $\frac{5000}{10000} = 0.5$

Step 3: Distribute the profit

Now, we distribute the total profit of $1920 according to these ratios:

• The man who invested $2000 should receive: $0.2 \times 1920 = 384$

Answer:

The man who invested $2000 should receive $384 from the profit.

Would you like further details or have any questions?

Here are five related questions:

1. How much will the man who invested $3000 receive?
2. How much will the man who invested $5000 receive?
3. How would the profit distribution change if the total profit was $3000 instead of $1920?
4. What if a fourth person invested $4000—how would the profits be divided then?
5. How would a loss of $1920 be distributed based on the investments?

Tip: Always verify if ratios sum up to 1 when distributing profits to ensure correctness.