13. 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?
Answer: D
The ratio of profit sharing at the end of the year is 15:12:17.
The profit sharing ratio among the friends A, B, and C is determined to be 15:12:17 based on their respective investments and the duration of those investments.
A) 5:02:06
This option does not accurately reflect the final profit sharing ratio. Given the changes in investments and the time each friend’s money was invested, 5:02:06 does not correspond to the calculated investments and their respective durations.
B) 9:05:12
This ratio fails to represent the actual contributions of the friends after the adjustments to their investments. The profit sharing should account for the additional contributions made by A and the withdrawal by C, which is not captured in this option.
C) 10:06:15
While this option presents a ratio that appears balanced, it does not align with the final investments made by A, B, and C after 6 months. The profit sharing ratio must reflect the weighted time of the investments, which this option does not accurately depict.
D) 15:12:17
This option correctly represents the profit sharing ratio after considering the initial investments and the changes that occurred after 6 months. A's additional investment and C's withdrawal were properly factored into the final ratio, resulting in a fair distribution of profit among the three friends.
E) 18:16:25
This option is incorrect as it does not account for the changes in investment amounts and time. The ratio of 18:16:25 does not correspond to the actual investments made by A, B, and C after their respective adjustments.
Conclusion
The correct profit sharing ratio is 15:12:17, which accurately reflects the contributions made by A, B, and C, adjusted for time. Each option that deviates from this reflects a misunderstanding of how changes in investment and timing affect profit distribution, thereby failing to represent the actual financial contributions of each friend.