Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit ?

Options

A. A) 10110
B. B) 10500
C. C) 12000
D. D) 13000

Answer

To find Simran's share in the profit, we need to calculate the effective capital contribution of both Simran and Nanda over the time they invested in the business. Here's a step-by-step solution:

### Step 1: Calculate Simran's Investment Contribution
Simran invested Rs. 50,000 for 3 years (36 months).

\[ \text{Simran's contribution} = \text{Investment} \times \text{Time} = 50,000 \times 36 = 1,800,000 \]

### Step 2: Calculate Nanda's Investment Contribution
Nanda joined after 6 months, so she invested her capital for 2.5 years (30 months).

\[ \text{Nanda's contribution} = \text{Investment} \times \text{Time} = 80,000 \times 30 = 2,400,000 \]

### Step 3: Calculate the Total Contribution
Now, we add both contributions to find the total contribution:

\[ \text{Total Contribution} = \text{Simran's contribution} + \text{Nanda's contribution} = 1,800,000 + 2,400,000 = 4,200,000 \]

### Step 4: Calculate the Ratio of Contributions
Now we find the ratio of Simran's contribution to Nanda's contribution:

\[ \text{Ratio} = \frac{\text{Simran's contribution}}{\text{Nanda's contribution}} = \frac{1,800,000}{2,400,000} = \frac{3}{4} \]

### Step 5: Calculate Simran's Share in Profit
The total profit earned is Rs. 24,500. To find Simran's share, we use the ratio calculated in the previous step.

\[ \text{Simran's Share} = \frac{3}{3 + 4} \times 24,500 = \frac{3}{7} \times 24,500 \]

Calculating this gives:

\[ \text{Simran's Share} = \frac{3 \times 24,500}{7} = \frac{73,500}{7} = 10,500 \]

### Final Answer
Simran's share in the profit is Rs. 10,500.

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