To solve the problem step-by-step, we will first denote the investments of A, B, and C and then set up equations based on the information given.
### Step 1: Define the Variables
Let:
- A's investment = \( x \)
- B's investment = \( x + 50,000 \) (since B invested Rs. 50,000 more than A)
- C's investment = \( (x + 50,000) - 25,000 = x + 25,000 \) (since C invested Rs. 25,000 less than B)
### Step 2: Set Up the Total Investment Equation
According to the problem, the total investment is Rs. 3,00,000. Therefore, we can write the equation:
\[
x + (x + 50,000) + (x + 25,000) = 3,00,000
\]
### Step 3: Simplify the Equation
Combine like terms:
\[
x + x + 50,000 + x + 25,000 = 3,00,000
\]
This simplifies to:
\[
3x + 75,000 = 3,00,000
\]
### Step 4: Solve for \( x \)
Subtract 75,000 from both sides:
\[
3x = 3,00,000 - 75,000
\]
\[
3x = 2,25,000
\]
Now, divide by 3:
\[
x = \frac{2,25,000}{3} = 75,000
\]
### Step 5: Calculate Individual Investments
Now that we have \( x \):
- A's investment = \( x = 75,000 \)
- B's investment = \( x + 50,000 = 75,000 + 50,000 = 1,25,000 \)
- C's investment = \( x + 25,000 = 75,000 + 25,000 = 1,00,000 \)
### Step 6: Determine the Profit Sharing Ratio
The profit is shared in the ratio of their investments:
- A's investment = 75,000
- B's investment = 1,25,000
- C's investment = 1,00,000
The ratio of their investments is:
\[
75,000 : 1,25,000 : 1,00,000
\]
To simplify this ratio, we can divide each term by 25,000:
\[
3 : 5 : 4
\]
### Step 7: Calculate the Total Parts in the Ratio
The total parts in the ratio = \( 3 + 5 + 4 = 12 \)
### Step 8: Calculate C's Share of the Profit
The total profit is Rs. 14,400. To find C's share:
- C's share in the profit = \( \frac{4}{12} \times 14,400 \)
Calculating this:
\[
C's \, share = \frac{4}{12} \times 14,400 = \frac{1}{3} \times 14,400 = 4,800
\]
### Final Answer
C's share of the profit is Rs. 4,800.
---
