https://file.aiquickdraw.com/mathbot/file/1729969218529uphd773i.jpg

Let's break down and solve this problem step-by-step.

### Problem Interpretation and Setup

Given:
1. Three partners: \( P \), \( Q \), and \( R \).
2. Conditions on their capitals:
   - Twice of \( P \)'s capital is equal to thrice of \( Q \)'s capital.
   - \( Q \)'s capital is four times \( R \)'s capital.
3. A total profit of ₹27,500, and we need to find \( Q \)'s share.

Let's denote:
- \( P \)'s capital as \( P \),
- \( Q \)'s capital as \( Q \),
- \( R \)'s capital as \( R \).

### Step 1: Set Up the Equations

From the information given:
1. **Twice of \( P \)'s capital is equal to thrice of \( Q \)'s capital:**
   \[
   2P = 3Q
   \]

2. **\( Q \)'s capital is four times \( R \)'s capital:**
   \[
   Q = 4R
   \]

### Step 2: Express \( P \) and \( Q \) in Terms of \( R \)

From \( Q = 4R \):
- Substitute \( Q \) in terms of \( R \) in the first equation.

Substitute \( Q = 4R \) into \( 2P = 3Q \):
\[
2P = 3(4R)
\]
\[
2P = 12R
\]
\[
P = 6R
\]

Thus, we have:
- \( P = 6R \)
- \( Q = 4R \)
- \( R = R \) (already in terms of itself)

### Step 3: Calculate the Ratio of Capitals

The capitals of \( P \), \( Q \), and \( R \) are in the ratio:
\[
P : Q : R = 6R : 4R : R = 6 : 4 : 1
\]

### Step 4: Divide the Profit According to This Ratio

The total profit is ₹27,500, and we need to split it in the ratio \( 6 : 4 : 1 \).

The sum of the parts is:
\[
6 + 4 + 1 = 11
\]

So, \( Q \)'s share is:
\[
Q = \frac{4}{11} \times 27500
\]

### Step 5: Calculate \( Q \)'s Share

\[
Q = \frac{4 \times 27500}{11} = 10000
\]

### Answer
The correct answer is **₹10,000**.

---

Would you like additional details on any of these steps or have any questions?

### Further Questions
1. How would the solution change if the profit was different?
2. What if the ratio of capitals had a different multiplier?
3. How can you verify that the capital allocation was correct?
4. Could this be solved using percentages instead of ratios?
5. What if one partner withdrew some capital during the year?

### Tip
When dealing with profit-sharing problems, always start by establishing the ratio based on given conditions before calculating specific shares.

Three partners P, Q, and R start a business. Twice of P's capital is equal to thrice of Q's capital, and Q's capital is four times R's capital. Out of a total profit of ₹27,500 at the end of the year, Q's share is:

Calculate Q's share in a business profit distribution problem where three partners P, Q, and R invest with capital ratios derived from given conditions. Learn how to determine individual shares based on proportional ratios, with a total profit of ₹27,500.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation