To solve the problem step by step, we will determine the annual profit based on the investments made by A, B, and C, and the given conditions.
### Step 1: Calculate the effective capital contribution of each partner.
- **A's investment:** A invested Rs 28,000 for 5 months.
- Effective capital = 28,000 * 5 = Rs 140,000 (capital months)
- **A's remaining investment:** After 5 months, A withdrew Rs 8,000, leaving Rs 20,000 to be invested for the remaining 7 months.
- Effective capital after withdrawal = 20,000 * 7 = Rs 140,000 (capital months)
- **B's investment:** B joined after 5 months with Rs 24,000 for 7 months.
- Effective capital = 24,000 * 7 = Rs 168,000 (capital months)
- **C's investment:** C joined with Rs 32,000 for 7 months.
- Effective capital = 32,000 * 7 = Rs 224,000 (capital months)
### Step 2: Calculate the total effective capital contributions.
Now, we sum up the effective capital contributions:
- Total effective capital for A = Rs 140,000 + Rs 140,000 = Rs 280,000
- Total effective capital for B = Rs 168,000
- Total effective capital for C = Rs 224,000
### Step 3: Find the profit-sharing ratio.
The profit-sharing ratio of A, B, and C can be calculated as follows:
- A's share = 280,000
- B's share = 168,000
- C's share = 224,000
To simplify the ratio, we can divide each amount by 56,000 (the GCD):
- A : B : C = 280,000 / 56,000 : 168,000 / 56,000 : 224,000 / 56,000
- A : B : C = 5 : 3 : 4
### Step 4: Set up the equation based on the profit difference.
Let the total annual profit be X. According to the problem, the difference between A's share and B's share is Rs 2,400.
- A's share = (5/12) * X
- B's share = (3/12) * X
The difference can be expressed as:
\[
\frac{5}{12}X - \frac{3}{12}X = 2400
\]
### Step 5: Solve for X.
Simplifying the left side:
\[
\frac{2}{12}X = 2400
\]
This simplifies to:
\[
\frac{1}{6}X = 2400
\]
Now, multiply both sides by 6:
\[
X = 2400 * 6
\]
\[
X = 14400
\]
### Conclusion
The annual profit received is Rs 14,400.
