A, B and C subscribe Rs. 47000 for a business.If a subscribes Rs. 7000 more than B and B Rs. 5000 more than C, then out of total profit of Rs. 4700, C receive:

Options

A. Rs. 1200
B. Rs. 4500
C. Rs. 1000
D. None of these

Answer

To solve the problem step by step, we will first determine the amounts subscribed by A, B, and C based on the information provided, and then calculate how much C will receive from the total profit.

### Step 1: Define the variables
Let:
- C's subscription = x
- B's subscription = x + 5000 (since B subscribes Rs. 5000 more than C)
- A's subscription = (x + 5000) + 7000 = x + 12000 (since A subscribes Rs. 7000 more than B)

### Step 2: Set up the equation
According to the problem, the total subscription by A, B, and C is Rs. 47000. Therefore, we can write the equation:
\[ A + B + C = 47000 \]
Substituting the values we defined:
\[ (x + 12000) + (x + 5000) + x = 47000 \]

### Step 3: Simplify the equation
Combine like terms:
\[ 3x + 17000 = 47000 \]

### Step 4: Solve for x
Subtract 17000 from both sides:
\[ 3x = 47000 - 17000 \]
\[ 3x = 30000 \]
Now, divide by 3:
\[ x = 10000 \]

### Step 5: Calculate the subscriptions
Now that we have x, we can find the amounts subscribed by A, B, and C:
- C's subscription = x = Rs. 10000
- B's subscription = x + 5000 = 10000 + 5000 = Rs. 15000
- A's subscription = x + 12000 = 10000 + 12000 = Rs. 22000

### Step 6: Determine the profit-sharing ratio
The profit-sharing ratio is based on their subscriptions:
- A's share = Rs. 22000
- B's share = Rs. 15000
- C's share = Rs. 10000

### Step 7: Calculate the total parts
Total parts = A + B + C = 22000 + 15000 + 10000 = Rs. 47000 (which confirms our calculations)

### Step 8: Calculate the profit per unit
Total profit = Rs. 4700
Total parts = 22000 + 15000 + 10000 = 47000
The profit per unit is:
\[ \text{Profit per unit} = \frac{4700}{47000} = 0.1 \]

### Step 9: Calculate C's share of the profit
C's share of the profit is based on his subscription:
C's subscription = Rs. 10000 corresponds to 10 parts (since Rs. 10000 is 10% of Rs. 100000).
Thus, C's share of the profit is:
\[ C's \text{ profit} = 10 \times 0.1 \times 4700 = Rs. 1000 \]

### Final Answer
C receives Rs. 1000 from the total profit.

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