A, B and C are three partners in a business. The profit share of A is 3/16 of the profit and B's share is 1/4 of the profit. If C receives Rs. 243, then the amount received by B will be:

Answer

To solve the problem step by step, we will first determine the total profit based on the shares of A, B, and C, and then find the amount received by B.

### Step 1: Determine the shares of A and B
- A's share = \( \frac{3}{16} \) of the total profit (let's denote total profit as \( P \)).
- B's share = \( \frac{1}{4} \) of the total profit.

### Step 2: Convert B's share to a fraction with a common denominator
- To add A's and B's shares, we need a common denominator. The common denominator for 16 and 4 is 16.
- B's share in terms of 16:
\[ B's \, share = \frac{1}{4} = \frac{4}{16} \]

### Step 3: Calculate the total share of A and B
- Now, we can add A's and B's shares:
\[ A's \, share + B's \, share = \frac{3}{16} + \frac{4}{16} = \frac{7}{16} \]

### Step 4: Determine C's share
- Since A and B together receive \( \frac{7}{16} \) of the total profit, C's share can be calculated as:
\[ C's \, share = 1 - (A's \, share + B's \, share) = 1 - \frac{7}{16} = \frac{16}{16} - \frac{7}{16} = \frac{9}{16} \]

### Step 5: Set up the equation based on C's share
- We know that C receives Rs. 243, which corresponds to \( \frac{9}{16} \) of the total profit:
\[ \frac{9}{16} P = 243 \]

### Step 6: Solve for the total profit \( P \)
- To find \( P \), we can rearrange the equation:
\[ P = 243 \times \frac{16}{9} \]
- Calculating \( P \):
\[ P = 243 \times \frac{16}{9} = 243 \div 9 \times 16 = 27 \times 16 = 432 \]

### Step 7: Calculate B's share
- Now that we have the total profit \( P = 432 \), we can find B's share:
\[ B's \, share = \frac{1}{4} P = \frac{1}{4} \times 432 = 108 \]

### Final Answer
- The amount received by B is Rs. 108.