Kanti started a business investing Rs. 9000. Five months later, Sudhakar joined him by investing Rs. 8000. If they make a profit of Rs. 6970 at the end of year . Sudhakar's share of profit is -

Options

A. Rs. 3690
B. Rs. 1883.78
C. Rs. 2380
D. Rs. 3864

Answer

To find Sudhakar's share of the profit, we will follow these steps:

### Step 1: Calculate the effective investment of both partners.
Kanti invested Rs. 9000 for the entire year (12 months), while Sudhakar invested Rs. 8000 but joined 5 months later, meaning he invested for only 7 months.

- Kanti's investment in terms of "months" = 9000 * 12 = 108000
- Sudhakar's investment in terms of "months" = 8000 * 7 = 56000

### Step 2: Determine the ratio of their investments.
Now, we find the ratio of their effective investments:

- Kanti's effective investment = 108000
- Sudhakar's effective investment = 56000

The ratio of their investments is:
\[ \text{Kanti : Sudhakar} = 108000 : 56000 \]

To simplify this ratio, we can divide both sides by 2000:
\[ \text{Kanti : Sudhakar} = 54 : 28 \]

Further simplifying gives:
\[ \text{Kanti : Sudhakar} = 27 : 14 \]

### Step 3: Calculate the total parts in the profit sharing.
The total parts of the profit are:
\[ 27 + 14 = 41 \]

### Step 4: Calculate Sudhakar's share of the profit.
The total profit is Rs. 6970. To find Sudhakar's share, we use the ratio of his investment:

Sudhakar's share of the profit is given by:
\[ \text{Sudhakar's Share} = \left( \frac{14}{41} \right) \times 6970 \]

Calculating this:
\[ \text{Sudhakar's Share} = \frac{14 \times 6970}{41} \]

Calculating \( \frac{6970}{41} \):
\[ 6970 \div 41 = 170 \]

Now, multiplying by 14:
\[ \text{Sudhakar's Share} = 14 \times 170 = 2380 \]

### Final Answer:
Sudhakar's share of the profit is Rs. 2380.

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