Rakesh invests Rs. 70,000. After 8 months, Vinod joins with Rs. 1,80,000. In what ratio should the year-end profit be divided?

Introduction / Context:
When partners invest at different times, compute time-weighted capitals to obtain the profit-sharing ratio. Here, one partner joins late with a larger capital for fewer months.

Given Data / Assumptions:

• Rakesh: Rs. 70,000 for 12 months.
• Vinod: Rs. 1,80,000 for 4 months (joined after 8 months).
• Profits divide in proportion to capital * time.

Concept / Approach:
Compute each partner’s product capital * months, then reduce to the simplest ratio for profit division.

Step-by-Step Solution:
Rakesh weight = 70,000 * 12 = 840,000. Vinod weight = 1,80,000 * 4 = 720,000. Ratio Rakesh : Vinod = 840,000 : 720,000 = 7 : 6.

Verification / Alternative check:
Divide both by 120,000 to get 7 : 6. No listed option equals 7 : 6, confirming “None of these.”

Why Other Options Are Wrong:
8 : 7, 6 : 5, or 7 : 5 disagree with the precise time-weighted calculation.

Common Pitfalls:
Using 8 months for Vinod instead of 4, or comparing capital values without adjusting for time. Always multiply capital by the number of months invested.

Final Answer:
None of these