Vishal and Raghu jointly start a business. Vishal invests three times as much money as Raghu and keeps his money invested for twice the time as Raghu. If the gain is proportional to both money invested and time, Raghu receives Rs. 4,000 as his share of the profit. What is the total profit earned by the business?

Introduction / Context:
This question tests understanding of profit sharing in partnerships where both the amount of capital and the duration of investment affect the share of profit. The scenario involves two partners, Vishal and Raghu, with a specific relation between their capital amounts and the times for which they are invested. We are given Raghu's actual profit and must determine the total profit of the business.

Given Data / Assumptions:

• Vishal and Raghu start the business together.
• Vishal invests three times the capital of Raghu.
• Vishal invests his money for double the time compared to Raghu.
• Raghu receives Rs. 4,000 as his share of profit.
• Profit is proportional to capital multiplied by time.

Concept / Approach:
The fundamental rule is that profit share is proportional to (capital * time). When one partner invests more money and keeps it invested longer, that partner receives a correspondingly larger share of the profit. By forming a ratio of their effective investments, we can find the ratio of their profit shares. Once we know how Raghu's share relates to total profit, we can directly compute the total profit.

Step-by-Step Solution:
Step 1: Let Raghu's capital be R and his time be T.Step 2: Then Vishal's capital is 3R and his time is 2T.Step 3: Raghu's capital time is R * T.Step 4: Vishal's capital time is 3R * 2T = 6RT.Step 5: Therefore, their profit share ratio Raghu : Vishal is RT : 6RT = 1 : 6.Step 6: Total profit is divided into 1 + 6 = 7 equal parts, with Raghu receiving 1 part and Vishal receiving 6 parts.Step 7: Given Raghu's share is Rs. 4,000, which equals 1 part, so total profit = 7 * 4,000 = Rs. 28,000.

Verification / Alternative check:
If total profit is Rs. 28,000, then Vishal's share should be 6 parts, that is 6 * 4,000 = Rs. 24,000. The ratio of 4,000 : 24,000 simplifies to 1 : 6, which matches the capital time ratio derived from the data. This confirms that the total profit of Rs. 28,000 is consistent with the partnership conditions.

Why Other Options Are Wrong:
If the total profit were Rs. 18,000, Raghu's share at 1/7 of the total would be about Rs. 2,571, not Rs. 4,000. For Rs. 14,000, his share would be only Rs. 2,000. For Rs. 8,000, his share would be approximately Rs. 1,143. None of these values match Raghu's given share of Rs. 4,000, so they are incorrect. 'None of these' is not needed because one of the given amounts is exactly correct.

Common Pitfalls:
Many learners incorrectly treat the profit ratio as simply 3 : 1 instead of combining the effect of both capital and time. Another mistake is to divide 4,000 by 3 or 2 directly without first determining the correct ratio of 1 : 6 and the total of 7 parts. Careful attention to both capital and time is essential in partnership questions.

Final Answer:
The total profit earned by the business is Rs. 28,000.