The ratio of investments of P and Q is `4 : 5`. P invests for 1 year and Q invests for 2 years. What is the ratio of profit of P and Q?

Options

A. `3:5`
B. `4:7`
C. `2:5`
D. `1:2`

Answer

To solve the problem, we need to find the ratio of profits of P and Q based on their investments and the time for which they invested.

### Step-by-Step Solution:

1. **Identify the Investments and Time**:
- The ratio of investments of P and Q is given as \(4 : 5\).
- P invests for 1 year, and Q invests for 2 years.

2. **Define Variables**:
- Let the investment of P be \(4x\) and the investment of Q be \(5x\), where \(x\) is a common multiplier.

3. **Calculate the Effective Investment**:
- The profit is proportional to the product of investment and time.
- For P, the effective investment is:
\[ \text{Effective Investment of P} = \text{Investment of P} \times \text{Time of P} = 4x \times 1 = 4x \]
- For Q, the effective investment is:
\[ \text{Effective Investment of Q} = \text{Investment of Q} \times \text{Time of Q} = 5x \times 2 = 10x \]

4. **Set Up the Profit Ratio**:
- The ratio of profits of P and Q can be expressed as:
\[ \text{Profit Ratio} = \frac{\text{Effective Investment of P}}{\text{Effective Investment of Q}} = \frac{4x}{10x} \]

5. **Simplify the Ratio**:
- The \(x\) cancels out:
\[ \text{Profit Ratio} = \frac{4}{10} = \frac{2}{5} \]

6. **Conclusion**:
- Therefore, the ratio of profits of P and Q is \(2 : 5\).

### Final Answer:
The ratio of profit of P and Q is \(2 : 5\).

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