A profit of 12% is made when a mobile phone is sold at P and there is 4% loss when the phone is sold at Rs Q. Then Q: Pis:

Options

A. `4:5`
B. `3:1`
C. `1:1`
D. `6:7`

Answer

To solve the problem, we need to find the ratio of Q to P given the profit and loss percentages when a mobile phone is sold at these prices.

### Step-by-Step Solution:

1. **Understanding the Profit and Loss:**
- When the mobile phone is sold at price P, there is a profit of 12%.
- When it is sold at price Q, there is a loss of 4%.

2. **Setting Up the Equations:**
- Let the cost price (CP) of the mobile phone be 100 (this is a common practice to simplify calculations).
- Selling Price (SP) when sold at P:
\[ P = CP + \text{Profit} = 100 + 12\% \text{ of } 100 = 100 + 12 = 112 \]
- Selling Price (SP) when sold at Q:
\[ Q = CP - \text{Loss} = 100 - 4\% \text{ of } 100 = 100 - 4 = 96 \]

3. **Finding the Ratio of Q to P:**
- Now we need to find the ratio \( \frac{Q}{P} \):
\[ \frac{Q}{P} = \frac{96}{112} \]

4. **Simplifying the Ratio:**
- To simplify \( \frac{96}{112} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD).
- The GCD of 96 and 112 is 16.
- So, we divide both by 16:
\[ \frac{96 \div 16}{112 \div 16} = \frac{6}{7} \]

5. **Final Ratio:**
- Therefore, the ratio \( Q : P \) is:
\[ Q : P = 6 : 7 \]

### Conclusion:
The ratio \( Q : P \) is \( 6 : 7 \).