Three friends, A, B, and C, invest money in the ratio 2:3:5. After 6 months, A invests another amount equaling $35,000, while C withdraws $15,000. The ratio of investments then changes to 11:6:7. What is the ratio of profit sharing at the end of the year if profit sharing is determined by the amount of money invested weighted by the time spent in the investment?

Rationale

The ratio of profit sharing at the end of the year is 15:12:17.

To determine the profit-sharing ratio of A, B, and C, we must consider both the initial investments and any changes made during the year. After accounting for A's additional investment and C's withdrawal, the final ratio reflects their weighted contributions over the time periods they remained invested.

A (5:02:06) YOUR ANSWER

This ratio does not accurately represent the adjusted contributions of A, B, and C after their respective changes in investment. The calculations based on the time and amount invested do not support such a low ratio for profit sharing.

B (9:05:12) YOUR ANSWER

While this ratio suggests some level of proportionality, it fails to align with the final contributions of A, B, and C after accounting for the changes in their investments. The time-weighted investments lead to a different profit-sharing distribution.

C (10:06:15) YOUR ANSWER

Although this ratio may seem plausible, it does not reflect the actual distribution of investments after A's additional investment and C's withdrawal. The calculations yield different values for each friend's contribution, leading to an incorrect profit-sharing ratio.

D (15:12:17) CORRECT

This ratio accurately reflects the final amounts invested by A, B, and C after the adjustments. Each friend's investment was weighted by the time they remained invested, leading to the correct profit-sharing distribution based on their contributions.

E (18:16:25) YOUR ANSWER

This ratio does not consider the changes in investment amounts and the time they were held. The values presented do not match the weighted contributions based on the time and amounts invested by A, B, and C throughout the year.

Conclusion

The final profit-sharing ratio of 15:12:17 is derived from the weighted investments of A, B, and C, taking into account both the initial ratios and subsequent changes. A's additional investment and C's withdrawal significantly impact the overall profit-sharing distribution, confirming that the adjustments correctly reflect their contributions over time. Hence, the chosen ratio accurately represents each friend's share of the profit at the end of the year.

The ratio of profit sharing at the end of the year is 15:12:17.

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