The ratio of two partners A and B is 2:3 . If they share the profit of Rs. 3000. What will be their shares ?

Options

A. `1200,1800`
B. `600 , 1200`
C. `1800 ,2400`
D. `300,700`

Answer

To solve the problem of finding the shares of partners A and B based on their profit-sharing ratio, we can follow these steps:

### Step 1: Understand the ratio
The ratio of the two partners A and B is given as 2:3. This means that for every 2 parts A receives, B receives 3 parts.

### Step 2: Calculate the total parts in the ratio
To find the total number of parts, we add the parts of A and B together:
\[ \text{Total parts} = 2 + 3 = 5 \]

### Step 3: Determine the total profit
The total profit to be shared between A and B is given as Rs. 3000.

### Step 4: Calculate A's share
To find A's share, we use the formula:
\[ \text{A's share} = \left(\frac{\text{A's ratio}}{\text{Total ratio}}\right) \times \text{Total profit} \]
Substituting the values:
\[ \text{A's share} = \left(\frac{2}{5}\right) \times 3000 \]
Calculating A's share:
\[ \text{A's share} = \frac{6000}{5} = 1200 \]

### Step 5: Calculate B's share
Similarly, we calculate B's share using the formula:
\[ \text{B's share} = \left(\frac{\text{B's ratio}}{\text{Total ratio}}\right) \times \text{Total profit} \]
Substituting the values:
\[ \text{B's share} = \left(\frac{3}{5}\right) \times 3000 \]
Calculating B's share:
\[ \text{B's share} = \frac{9000}{5} = 1800 \]

### Final Shares
- A's share = Rs. 1200
- B's share = Rs. 1800

### Summary
Thus, the shares of A and B from the profit of Rs. 3000 are:
- A's share: Rs. 1200
- B's share: Rs. 1800

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