In a partnership business, K and B start a business jointly. K invests Rs. 16,000 for 8 months, while B keeps his capital invested for 4 months. Out of the total profit, K receives 2/7 of the overall profit share. How much capital was contributed by B in rupees?

Introduction / Context:
This is a classic aptitude question based on the concept of partnership in business. In such questions, the profit is distributed among partners in proportion to the product of the capital invested and the time for which it is invested, commonly known as capital time or money months. Here, we are given the share of profit of one partner and the investment details, and we have to determine the capital contributed by the other partner.

Given Data / Assumptions:

• K and B are partners in a business.
• K invests Rs. 16,000 for 8 months.
• B keeps his capital invested for 4 months.
• K receives 2/7 of the total profit.
• Profit is distributed in the ratio of capital multiplied by time.

Concept / Approach:
The basic concept in partnership problems is that profit share is proportional to capital * time. If a partner invests more money or keeps it invested for more time, that partner should receive a higher share of the profit. Once we know the profit ratio between partners, we can equate it to the ratio of their capital time contributions and solve for the unknown capital.

Step-by-Step Solution:
Step 1: Compute K's capital time: 16,000 * 8 = 1,28,000 money months.Step 2: Let the capital of B be x. His capital time is x * 4 = 4x money months.Step 3: Since K receives 2/7 of the total profit, B must receive 5/7. Thus, the ratio of K : B profit shares is 2 : 5.Step 4: Profit share ratio equals capital time ratio, so 1,28,000 : 4x = 2 : 5.Step 5: Simplify 1,28,000 : 4x to 32,000 : x. Then 32,000 : x = 2 : 5 implies 32,000 / x = 2 / 5.Step 6: Cross multiply: 32,000 * 5 = 2x, hence 1,60,000 = 2x, so x = 80,000.

Verification / Alternative check:
Capital time for K is 1,28,000 and for B is 4 * 80,000 = 3,20,000. The ratio K : B is 1,28,000 : 3,20,000 = 2 : 5. Therefore, K receives 2 parts and B receives 5 parts of profit, so K's fraction of total profit is 2 / (2 + 5) = 2/7, which matches the given data.

Why Other Options Are Wrong:
Rs. 40,000, Rs. 64,000 and Rs. 96,000 do not give a capital time ratio of 2 : 5 when compared with K's investment. With these values, the resulting profit share of K would not be exactly 2/7 of the total profit. 'None of these' is also incorrect because one of the numerical options, Rs. 80,000, satisfies all the partnership conditions exactly.

Common Pitfalls:
Candidates often forget that profit distribution in partnership depends on both capital and time, not capital alone. Another frequent mistake is to interpret the 2/7 as the ratio between K and B, instead of K's fraction of the total profit. Mixing these interpretations leads to incorrect equations and wrong answers.

Final Answer:
The correct amount invested by B is Rs. 80,000.