Partnership with time-weighted capitals: Pramod starts a business with ₹ 40000. After 4 months, Vikas joins with ₹ 60000. At the end of 12 months, total profit is ₹ 16000. Find Vikas’s share in the profit.

Introduction / Context:
In partnership problems, profit is divided in the ratio of capital × time (money product). When partners join at different times, weight each investment by its active duration to get fair shares.

Given Data / Assumptions:

• Pramod: ₹ 40000 for 12 months.
• Vikas: ₹ 60000 for 8 months (since he joined after 4 months).
• Total profit = ₹ 16000.

Concept / Approach:
Compute money products and use them as share weights. Ratio = (40000*12) : (60000*8). Divide profit in this ratio to obtain Vikas’s share.

Step-by-Step Solution:
Pramod weight = 40000 * 12 = 480000.Vikas weight = 60000 * 8 = 480000.Weights ratio = 1 : 1. Total profit split equally.Vikas’s share = 16000 / 2 = ₹ 8000.

Verification / Alternative check:
If profit per weight unit is the same, equal weights imply equal profits. The computation confirms symmetry in money-time product.

Why Other Options Are Wrong:

• ₹ 4000 and ₹ 10000 require asymmetric weights, which are not present.
• ₹ 12000 contradicts equal weightage.

Common Pitfalls:

• Ignoring time and dividing profit only by capitals.
• Assuming equal months for both partners despite the staggered start.

Final Answer:
Rs. 8000