Arun, Kamal, and Vinay invest ₹8,000, ₹4,000, and ₹8,000 respectively. Arun withdraws after 6 months. If the total profit after 8 months is ₹4,005, what is Kamal's share?

Problem restatement
Compute each partner's time-weighted capital and then allocate the profit accordingly. Arun leaves at month 6; business ends at month 8.

Given data

• Arun: ₹8,000 for 6 months.
• Kamal: ₹4,000 for 8 months.
• Vinay: ₹8,000 for 8 months.
• Total profit = ₹4,005.

Concept/Approach
Shares ∝ capital × time (money-months).

Step-by-step calculation
Arun units = 8,000 × 6 = 48,000 Kamal units = 4,000 × 8 = 32,000 Vinay units = 8,000 × 8 = 64,000 Ratio = 48,000 : 32,000 : 64,000 = 3 : 2 : 4 Sum of parts = 3 + 2 + 4 = 9 One part = 4,005 ÷ 9 = 445 Kamal's share = 2 × 445 = ₹890

Verification
Arun's share = 3 × 445 = ₹1,335; Vinay's = 4 × 445 = ₹1,780; total = 1,335 + 890 + 1,780 = ₹4,005.

Common pitfalls

• Dividing profit by the raw capital ratio without time-weighting.

Final Answer
₹890