Partnership profits with unequal capital and time: A invests thrice as much as B and keeps the money for twice B’s period. If B’s profit share is Rs. 4,000, what is the total profit of the firm?

Introduction / Context:
In partnership questions, profit sharing is proportional to capital * time. Here A invests more money and for a longer period than B. We are given B’s profit and must compute the total profit of the business.

Given Data / Assumptions:

• A’s capital is 3 times B’s capital.
• A’s time in business is 2 times B’s time.
• B’s profit share = Rs. 4,000.
• Profits are divided in the ratio of (capital * time).

Concept / Approach:
If B’s capital is 1 unit for 1 unit of time, B’s weight = 1 * 1 = 1. A’s weight = 3 * 2 = 6. Therefore, A : B = 6 : 1. Total parts = 7. Each part equals B’s profit share since B has 1 part.

Step-by-Step Solution:
Profit ratio A : B = (3 * 2) : (1 * 1) = 6 : 1. Total parts = 6 + 1 = 7. 1 part = Rs. 4,000 (B’s share). Total profit = 7 * 4,000 = Rs. 28,000.

Verification / Alternative check:
A’s share = 6 * 4,000 = Rs. 24,000; B’s share = Rs. 4,000. Sum = Rs. 28,000, consistent with the ratio 6 : 1.

Why Other Options Are Wrong:
Rs. 24,000 and Rs. 20,000 underestimate total parts. Rs. 16,000 contradicts the given B’s share of Rs. 4,000.

Common Pitfalls:
Ignoring time in the ratio or adding the multipliers incorrectly. Always compute capital * time for each partner before forming the ratio.

Final Answer:
Rs. 28,000