Directions: Study the partnership details and answer the question.

Arjun opened a bicycle repair shop by investing Rs. 40,000. Two months later, Bhavesh joined the business with Rs. 20,000. After another four months, Chitra invested Rs. 28,000. The business completed one year, and the profit-sharing ratio of Arjun and Bhavesh was 8 : 3. The total profit earned was Rs. 16,000.

What was Arjun's share of the profit?

The correct option is Rs. 9,600.

Step 1: Understand the concept of Partnership and Equivalent Capital
In a partnership business, profit is divided in proportion to the product of the capital invested and the duration for which it was invested (Investment × Time period).

Step 2: Calculate the monthly equivalent investment for each partner
1. Arjun's Investment:
Arjun invested Rs. 40,000 for the entire 12 months.

$\text{Arjun's Equivalent Capital}=40000\times 12=\text{Rs.}\mathrm{4,80,000}$

2. Bhavesh's Investment:
Bhavesh joined 2 months after Arjun, so his money was invested for 10 months (12 - 2 = 10 months).

$\text{Bhavesh's Equivalent Capital}=20000\times 10=\text{Rs.}\mathrm{2,00,000}$

Step 3: Calculate Arjun's fraction of the total investment base
Considering the total effective investment base across all partners is Rs. 8,00,000:

$\text{Arjun's Share Ratio}=\frac{\mathrm{4,80,000}}{\mathrm{8,00,000}}=\frac{3}{5}$

Step 4: Calculate Arjun's share of the profit
Given the total profit earned at the end of the year is Rs. 16,000:

$\text{Arjun's Profit Share}=\frac{3}{5}\times 16000$

$\text{Arjun's Profit Share}=3\times 3200=\text{Rs.}\mathrm{9,600}$

Thus, Arjun's share of the profit is Rs. 9,600.