While selling a watch, a shopkeeper gives a discount of 15%. If he gives a discount of 20%, he earns Rs 51 less as profit. What is the original price of the watch?

Options

A. Rs 920
B. Rs 985
C. Rs 1125
D. Rs 1020

Answer

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

1. **Calculate Selling Price with 15% Discount:**
- If the shopkeeper gives a discount of 15%, the selling price (SP1) can be calculated as:
\[ SP1 = P - 0.15P = 0.85P \]

2. **Calculate Selling Price with 20% Discount:**
- If the shopkeeper gives a discount of 20%, the selling price (SP2) can be calculated as:
\[ SP2 = P - 0.20P = 0.80P \]

3. **Determine the Profit Difference:**
- According to the problem, the profit when selling at a 20% discount is Rs 51 less than the profit when selling at a 15% discount.
- Let’s denote the cost price (CP) of the watch as \( C \).
- The profit when selling at 15% discount is:
\[ \text{Profit1} = SP1 - C = 0.85P - C \]
- The profit when selling at 20% discount is:
\[ \text{Profit2} = SP2 - C = 0.80P - C \]

4. **Set Up the Equation:**
- According to the problem:
\[ \text{Profit1} - \text{Profit2 = 51} \]
- Substituting the profit expressions:
\[ (0.85P - C) - (0.80P - C) = 51 \]
- Simplifying this gives:
\[ 0.85P - 0.80P = 51 \]
\[ 0.05P = 51 \]

5. **Solve for Original Price \( P \):**
- To find \( P \), divide both sides by 0.05:
\[ P = \frac{51}{0.05} = 1020 \]

Thus, the original price of the watch is **Rs 1020**.