A trader purchases a watch and a wall clock for Rs 390. He sells them making a profit of 10% on the watch and 15% on the wall clock. He earns a profit of Rs 51.50. The difference between the original prices of the wall clock and the watch is equal to

Options

A. Rs110
B. Rs100
C. Rs80
D. Rs120

Answer

To solve the problem step by step, we will follow the information given in the question and the calculations as outlined in the video transcript.

### Step-by-Step Solution:

1. **Identify the Variables**:
- Let the cost price (CP) of the watch be \( X \).
- Therefore, the cost price (CP) of the wall clock will be \( 390 - X \) (since the total cost is Rs. 390).

2. **Calculate the Profit**:
- The profit on the watch is \( 10\% \) of \( X \), which can be expressed as:
\[ \text{Profit on watch} = \frac{10}{100} \times X = 0.1X \]
- The profit on the wall clock is \( 15\% \) of \( (390 - X) \), which can be expressed as:
\[ \text{Profit on wall clock} = \frac{15}{100} \times (390 - X) = 0.15(390 - X) \]

3. **Total Profit Calculation**:
- The total profit earned from both items is given as Rs. 51.50. Therefore, we can write the equation:
\[ 0.1X + 0.15(390 - X) = 51.50 \]

4. **Simplify the Equation**:
- Expanding the equation:
\[ 0.1X + 0.15 \times 390 - 0.15X = 51.50 \]
- Calculate \( 0.15 \times 390 \):
\[ 0.15 \times 390 = 58.5 \]
- Substitute this back into the equation:
\[ 0.1X + 58.5 - 0.15X = 51.50 \]
- Combine like terms:
\[ -0.05X + 58.5 = 51.50 \]

5. **Isolate \( X \)**:
- Subtract 58.5 from both sides:
\[ -0.05X = 51.50 - 58.5 \]
- Calculate \( 51.50 - 58.5 \):
\[ 51.50 - 58.5 = -7 \]
- So now we have:
\[ -0.05X = -7 \]
- Divide both sides by -0.05:
\[ X = \frac{-7}{-0.05} = 140 \]

6. **Find the Cost Price of the Wall Clock**:
- Now that we have \( X \) (the cost price of the watch), we can find the cost price of the wall clock:
\[ \text{CP of wall clock} = 390 - X = 390 - 140 = 250 \]

7. **Calculate the Difference Between the Original Prices**:
- The difference between the original prices of the wall clock and the watch is:
\[ \text{Difference} = 250 - 140 = 110 \]

### Final Answer:
The difference between the original prices of the wall clock and the watch is Rs. 110.

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