To solve the problem step by step, let's break down the investments and the time each partner spent in the business.
### Step 1: Calculate the effective capital contribution of each partner.
1. **Partner P**:
- Investment = Rs 30,000
- Time = 12 months (entire year)
- Effective capital contribution = 30,000 * 12 = Rs 360,000
2. **Partner Q**:
- Investment = Rs 40,000
- Time = 2 months (initially) + 6 months (after rejoining with 3/4 capital)
- Effective capital contribution for the first 2 months = 40,000 * 2 = Rs 80,000
- New investment after rejoining = 40,000 * (3/4) = Rs 30,000
- Effective capital contribution for the next 10 months = 30,000 * 10 = Rs 300,000
- Total effective capital contribution = Rs 80,000 + Rs 300,000 = Rs 380,000
3. **Partner R**:
- Investment = Rs 50,000
- Time = 3 months (initially) + 4 months (after rejoining with 4/5 capital)
- Effective capital contribution for the first 3 months = 50,000 * 3 = Rs 150,000
- New investment after rejoining = 50,000 * (4/5) = Rs 40,000
- Effective capital contribution for the next 9 months = 40,000 * 9 = Rs 360,000
- Total effective capital contribution = Rs 150,000 + Rs 360,000 = Rs 510,000
### Step 2: Calculate the total effective capital contributions.
- Total effective capital contributions = P + Q + R
- Total = Rs 360,000 + Rs 380,000 + Rs 510,000 = Rs 1,250,000
### Step 3: Determine the profit share of each partner.
The total profit is Rs 27,900. The profit share of each partner is proportional to their effective capital contributions.
1. **Profit share of P**:
- P's share = (360,000 / 1,250,000) * 27,900 = Rs 10,032
2. **Profit share of Q**:
- Q's share = (380,000 / 1,250,000) * 27,900 = Rs 11,064
3. **Profit share of R**:
- R's share = (510,000 / 1,250,000) * 27,900 = Rs 6,804
### Step 4: Calculate how much more R got than Q.
- Difference = R's share - Q's share = Rs 6,804 - Rs 11,064 = Rs -4,260
Since R's share is less than Q's, we need to find how much more Q got than R.
### Final Calculation:
- Q got more than R = Rs 11,064 - Rs 6,804 = Rs 4,260
### Conclusion:
R did not get more than Q; instead, Q got Rs 4,260 more than R.