While selling a watch, a shop keeper gives a discount of 5%. If he gives a discount of 6%, he earns Rs.15 less as profit. What is the marked price of the watch?

Options

A. Rs. 1250
B. Rs. 1400
C. Rs. 1500s
D. Rs. 750

Answer

To solve the problem step by step, we will denote the marked price of the watch as \( x \).

### Step 1: Calculate Selling Price with 5% Discount
When the shopkeeper gives a discount of 5%, the selling price (SP1) can be calculated as:
\[ SP1 = x - 0.05x = 0.95x \]

### Step 2: Calculate Selling Price with 6% Discount
When the shopkeeper gives a discount of 6%, the selling price (SP2) can be calculated as:
\[ SP2 = x - 0.06x = 0.94x \]

### Step 3: Set Up the Profit Equation
Let the cost price (CP) of the watch be \( CP \). The profit when selling at a 5% discount is:
\[ Profit1 = SP1 - CP = 0.95x - CP \]
The profit when selling at a 6% discount is:
\[ Profit2 = SP2 - CP = 0.94x - CP \]

According to the problem, the profit at a 6% discount is Rs. 15 less than the profit at a 5% discount:
\[ Profit2 = Profit1 - 15 \]
Substituting the expressions for profit:
\[ 0.94x - CP = (0.95x - CP) - 15 \]

### Step 4: Simplify the Equation
Now, we can simplify the equation:
\[ 0.94x - CP = 0.95x - CP - 15 \]
Cancelling \( CP \) from both sides:
\[ 0.94x = 0.95x - 15 \]
Rearranging gives:
\[ 0.94x - 0.95x = -15 \]
\[ -0.01x = -15 \]

### Step 5: Solve for Marked Price
Now, we can solve for \( x \):
\[ x = \frac{-15}{-0.01} = 1500 \]

### Conclusion
The marked price of the watch is:
\[ \boxed{1500} \]