Certainly! Let's break down the question and use the given information to find a detailed, step-by-step solution.
### Step-by-Step Solution
The partners [tex]\(P, Q,\)[/tex] and [tex]\(R\)[/tex] are sharing profits in the ratio of 2:3:5. We can denote their profit-sharing ratio as follows:
- Profit share of [tex]\(P\)[/tex] = 2 parts
- Profit share of [tex]\(Q\)[/tex] = 3 parts
- Profit share of [tex]\(R\)[/tex] = 5 parts
#### Step 1: Total Parts in the Profit Ratio
First, we calculate the total parts in the profit-sharing ratio by summing up the parts of [tex]\(P, Q,\)[/tex] and [tex]\(R\)[/tex].
[tex]\[
\text{Total parts} = 2 + 3 + 5 = 10
\][/tex]
#### Step 2: Assume a Total Profit for Calculation
For the purpose of our calculation, let's assume the total profit is 100 units. We use this assumed amount to simplify the calculations and understand the distribution of profits among the partners.
#### Step 3: Calculate the Profit Share for Each Partner
Now, let's use the profit-sharing ratio to determine the amount of profit each partner receives:
1. Profit Share of [tex]\(P\)[/tex]:
[tex]\[
\text{Profit of } P = \left(\frac{2}{10}\right) \times 100 = 20 \text{ units}
\][/tex]
2. Profit Share of [tex]\(Q\)[/tex]:
[tex]\[
\text{Profit of } Q = \left(\frac{3}{10}\right) \times 100 = 30 \text{ units}
\][/tex]
3. Profit Share of [tex]\(R\)[/tex]:
[tex]\[
\text{Profit of } R = \left(\frac{5}{10}\right) \times 100 = 50 \text{ units}
\][/tex]
### Conclusion
Thus, based on our assumed total profit of 100 units and the given profit ratio of 2:3:5, the distribution of the profit among the partners [tex]\(P, Q,\)[/tex] and [tex]\(R\)[/tex] is as follows:
- [tex]\(P\)[/tex] receives 20 units of profit.
- [tex]\(Q\)[/tex] receives 30 units of profit.
- [tex]\(R\)[/tex] receives 50 units of profit.
To summarize:
[tex]\[
\text{Total parts} = 10,\ \text{Profit of } P = 20 \text{ units},\ \text{Profit of } Q = 30 \text{ units},\ \text{Profit of } R = 50 \text{ units}
\][/tex]
This step-by-step approach ensures that we carefully distribute the profit according to the given ratio, providing a clear and thorough solution to the problem.
