https://file.aiquickdraw.com/mathbot/file/1726836016786r4hztig4.jpg

Let's break down the problem step by step.

### Given Information:
- A invests 5000, and B invests 2000 in a business.
- A is a working partner and takes 20% of the total profit as his salary.
- The remaining profit is divided between A and B according to their capital.
- A receives ₹38,000 more than B in total.

### Let the total profit be \( P \).

#### Step 1: A's salary (working partner compensation)
- A takes 20% of the total profit as salary:  
  \[
  \text{A's salary} = 0.2P
  \]

#### Step 2: Remaining profit
- The remaining profit after A’s salary:  
  \[
  \text{Remaining profit} = P - 0.2P = 0.8P
  \]
- This remaining profit is divided according to their capital. Since the ratio of A's and B's capital is \( 5000:2000 = 5:2 \), the profit will be divided in the same ratio.

#### Step 3: A and B's shares from the remaining profit
- A’s share from the remaining profit:  
  \[
  \text{A's share} = \frac{5}{5+2} \times 0.8P = \frac{5}{7} \times 0.8P = \frac{4P}{7}
  \]
- B’s share from the remaining profit:  
  \[
  \text{B's share} = \frac{2}{7} \times 0.8P = \frac{1.6P}{7}
  \]

#### Step 4: Total amount received by A and B
- Total amount A receives:  
  \[
  \text{A's total} = 0.2P + \frac{4P}{7}
  \]
  Simplifying:  
  \[
  \text{A's total} = 0.2P + 0.5714P = 0.7714P
  \]
- Total amount B receives:  
  \[
  \text{B's total} = \frac{1.6P}{7} = 0.2286P
  \]

#### Step 5: Condition given in the problem
- It is given that A receives ₹38,000 more than B:  
  \[
  0.7714P - 0.2286P = 38000
  \]
  Simplifying:  
  \[
  0.5428P = 38000
  \]
  Solving for \( P \):  
  \[
  P = \frac{38000}{0.5428} = 70000
  \]

### Conclusion:
The total profit \( P \) is ₹70,000.

---

Would you like more details or have any further questions?

Here are five related questions to deepen understanding:
1. How would the answer change if A's salary was 30% instead of 20%?
2. If B invested 3000 instead of 2000, how would the final profit distribution change?
3. What if both A and B were working partners and shared the salary equally?
4. How is the concept of proportional division useful in other areas of business mathematics?
5. Can you determine what percentage of the total profit B received?

**Tip**: Always verify if the total amount distributed equals the total profit, especially when multiple partners are involved.

A and B start a business with 5000 and 2000. If A is working partner and takes 20% of the total profit as his salary and the remaining profit is divided as per the capital. If in this process A received 38000 more than B, find the amount of total profit?

Learn how to solve a profit distribution problem where A and B invest different amounts in a business. A, the working partner, takes 20% of the profit as salary, and the remaining profit is divided by their capital. A receives ₹38,000 more than B. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation