a and b start a buisness with different capitals a was to get 15% of the profit as salary and the rest was to be divided in the ratio of their investments. had the entire profit been distributed in the ratio of their investments b would have got rs 1350 more that what he actially got. what is b's actual share of the profit?

Let's break down the problem step by step.

### Variables:
- Let \( P \) be the total profit.
- Let \( a \) and \( b \) represent their investments in the business.
- Let \( b \)'s actual share of the profit be \( x \).
- Let the ratio of \( a \)'s and \( b \)'s investments be \( a : b \).

### Problem Breakdown:

1. **A's Salary:**  
   \( a \) gets 15% of the total profit \( P \) as a salary.  
   So, \( a \) receives \( 0.15P \).

2. **Remaining Profit:**  
   The remaining profit, \( 0.85P \), is distributed between \( a \) and \( b \) in the ratio of their investments, \( a : b \).

3. **If Entire Profit Was Distributed According to Investments:**  
   If the entire profit \( P \) was distributed according to their investment ratio, \( b \) would have received \( x + 1350 \) because he would have received Rs 1350 more than what he actually got.

### Step-by-Step Calculation:

1. Let \( a \)'s investment be \( A \) and \( b \)'s investment be \( B \).
2. \( b \)'s actual share \( x \) comes from the remaining profit \( 0.85P \), distributed according to their investments.
   
   So,  
   \[
   b \text{'s actual share } x = \frac{B}{A + B} \times 0.85P
   \]
3. If the entire profit was distributed in the ratio of their investments, \( b \)'s share would be:
   \[
   b \text{'s share in this case} = \frac{B}{A + B} \times P
   \]
4. According to the problem, \( b \) would have received Rs 1350 more in this case, so:
   \[
   \frac{B}{A + B} \times P = x + 1350
   \]
5. Substituting \( x \) from step 2 into this equation, we get:
   \[
   \frac{B}{A + B} \times P = \frac{B}{A + B} \times 0.85P + 1350
   \]
6. Simplifying the equation:
   \[
   \frac{B}{A + B} \times P - \frac{B}{A + B} \times 0.85P = 1350
   \]
   \[
   \frac{B}{A + B} \times 0.15P = 1350
   \]
7. Solving for \( P \):
   \[
   P = \frac{1350 \times (A + B)}{0.15B}
   \]

Now, with this equation, we need more information about the ratio of \( a \) and \( b \)'s investments to proceed with exact calculations. Do you have that information, or should we proceed assuming some common ratios?

Learn how to calculate B's actual share of profit in a business scenario where profit is distributed based on investment ratios and a fixed salary deduction for A. Understand the application of ratio and proportion in real-world profit sharing scenarios. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation