sachin started a business with rs 25000.two months later vinod joined him with rs 30000 and a month after that ajith joined with rs 40000.sachin is a working partner and hence receives 10% of the profits as  commision.if sachin received a total amont of rs 18300 as profit(including his commission) how much more than vinod did ajith receive in the profit? (a) rs 240 (b) rs 2700 (c) rs 3100 (d) cannot be determined

Let's break down the problem step by step.

### Step 1: Identify Time Periods and Capital Investments
- **Sachin's investment** = ₹25,000
- **Vinod's investment** = ₹30,000 (joined after 2 months)
- **Ajith's investment** = ₹40,000 (joined 3 months after Sachin)
  
Assume the total duration is **12 months**.

- **Sachin's time** = 12 months
- **Vinod's time** = 10 months (joined after 2 months)
- **Ajith's time** = 9 months (joined after 3 months)

### Step 2: Calculate the Weighted Capital Contribution (Capital × Time)
The profit is divided in proportion to the capital × time:

- **Sachin**: \( 25,000 \times 12 = 3,00,000 \)
- **Vinod**: \( 30,000 \times 10 = 3,00,000 \)
- **Ajith**: \( 40,000 \times 9 = 3,60,000 \)

### Step 3: Total Share
The total contribution of all partners is:

\[
3,00,000 + 3,00,000 + 3,60,000 = 9,60,000
\]

### Step 4: Sachin's Commission and Total Profit
Sachin receives 10% of the total profit as a commission. Let the total profit be **P**.

Sachin received ₹18,300, including his 10% commission. Let’s break this down:

- Sachin’s 10% commission: \( \frac{10}{100} \times P = 0.1P \)
- His share from the remaining profit (after subtracting his commission): \( \frac{3,00,000}{9,60,000} \) of the remaining profit, i.e. \( \frac{3,00,000}{9,60,000} \times 0.9P \).

Thus, Sachin’s total profit:

\[
0.1P + \left( \frac{3,00,000}{9,60,000} \times 0.9P \right) = 18,300
\]

Simplifying this:

\[
0.1P + \left( \frac{3,00,000}{9,60,000} \times 0.9P \right) = 18,300
\]

\[
0.1P + \frac{3}{9.6} \times 0.9P = 18,300
\]

\[
0.1P + \frac{27}{96}P = 18,300
\]

\[
0.1P + 0.28125P = 18,300
\]

\[
0.38125P = 18,300
\]

\[
P = \frac{18,300}{0.38125} = 48,000
\]

Thus, the total profit is **₹48,000**.

### Step 5: Calculate Vinod's and Ajith's Share of the Profit
After Sachin’s commission, the remaining profit is:

\[
0.9 \times 48,000 = 43,200
\]

Now, this remaining profit will be divided between Sachin, Vinod, and Ajith in the ratio of their capital contributions.

- Sachin’s share from the remaining profit: \( \frac{3,00,000}{9,60,000} \times 43,200 = 13,500 \)
- Vinod’s share: \( \frac{3,00,000}{9,60,000} \times 43,200 = 13,500 \)
- Ajith’s share: \( \frac{3,60,000}{9,60,000} \times 43,200 = 16,200 \)

### Step 6: Difference Between Ajith's and Vinod's Share
The difference between Ajith’s and Vinod’s share is:

\[
16,200 - 13,500 = 2,700
\]

### Conclusion
Ajith received ₹2,700 more than Vinod. Therefore, the correct answer is **(b) ₹2,700**.

Would you like more details on any part of this explanation?

---

Here are 5 related questions to expand your understanding:

1. How would the profit distribution change if Vinod joined after 3 months instead of 2?
2. What would be Sachin's profit share if his commission was 15% instead of 10%?
3. How would the total profit change if Ajith had invested ₹50,000 instead of ₹40,000?
4. What if Sachin and Vinod had invested equal amounts, how would the shares differ?
5. How does the duration of a partner's participation affect their profit share?

**Tip**: In profit-sharing problems, always account for both the capital invested and the time of participation when calculating shares.

Sachin started a business with Rs 25,000. Two months later, Vinod joined him with Rs 30,000, and a month after that, Ajith joined with Rs 40,000. Sachin is a working partner and hence receives 10% of the profits as commission. If Sachin received a total amount of Rs 18,300 as profit (including his commission), how much more than Vinod did Ajith receive in the profit? (a) Rs 240 (b) Rs 2,700 (c) Rs 3,100 (d) Cannot be determined.

Learn how to calculate the profit distribution in a business where partners join at different times with different investments. This step-by-step solution includes commission calculations, proportional profit sharing, and explains how Ajith received Rs 2,700 more than Vinod.

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