By selling a watch at a profit of 10 per cent, a man got Rs 15 more than half its price. What is the price of the watch?

Options

A. 10
B. 15
C. 25
D. 5

Answer

To find the price of the watch, let's denote the cost price of the watch as \( CP \).

1. **Understanding the profit**: The man sells the watch at a profit of 10%. Therefore, the selling price \( SP \) can be calculated as:
\[ SP = CP + 10\% \text{ of } CP = CP + 0.1 \times CP = 1.1 \times CP \]

2. **Setting up the equation**: According to the problem, the selling price is also equal to Rs 15 more than half of its price. This can be expressed as:
\[ SP = \frac{CP}{2} + 15 \]

3. **Equating the two expressions for selling price**: Now, we can set the two expressions for \( SP \) equal to each other:
\[ 1.1 \times CP = \frac{CP}{2} + 15 \]

4. **Eliminating the fraction**: To eliminate the fraction, we can multiply the entire equation by 2:
\[ 2 \times (1.1 \times CP) = CP + 30 \]
This simplifies to:
\[ 2.2 \times CP = CP + 30 \]

5. **Rearranging the equation**: Now, we can rearrange the equation to isolate \( CP \):
\[ 2.2 \times CP - CP = 30 \]
This simplifies to:
\[ 1.2 \times CP = 30 \]

6. **Solving for \( CP \)**: Finally, we can solve for \( CP \) by dividing both sides by 1.2:
\[ CP = \frac{30}{1.2} = 25 \]

7. **Conclusion**: Therefore, the price of the watch is Rs 25.