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

Options

A. ₹ 1250
B. ₹ 1400
C. ₹ 1500
D. ₹ 750

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Understand the given data
We have the following information:
- Discount 1 (d1) = 5%
- Discount 2 (d2) = 6%
- The difference in profit when the discounts change is ₹15.

### Step 2: Define the marked price
Let the marked price of the watch be denoted as \( M \).

### Step 3: Calculate the selling prices
1. **Selling Price with 5% discount (SP1)**:
\[ SP1 = M - (5\% \text{ of } M) = M - 0.05M = 0.95M \]

2. **Selling Price with 6% discount (SP2)**:
\[ SP2 = M - (6\% \text{ of } M) = M - 0.06M = 0.94M \]

### Step 4: Define the cost price
Let the cost price of the watch be denoted as \( C \).

### Step 5: Calculate the profits
1. **Profit with 5% discount (P1)**:
\[ P1 = SP1 - C = 0.95M - C \]

2. **Profit with 6% discount (P2)**:
\[ P2 = SP2 - C = 0.94M - C \]

### Step 6: Set up the equation based on the profit difference
According to the problem, the difference in profit when the discount changes from 5% to 6% is ₹15:
\[ P1 - P2 = 15 \]
Substituting the expressions for \( P1 \) and \( P2 \):
\[ (0.95M - C) - (0.94M - C) = 15 \]

### Step 7: Simplify the equation
The cost price \( C \) cancels out:
\[ 0.95M - 0.94M = 15 \]
This simplifies to:
\[ 0.01M = 15 \]

### Step 8: Solve for the marked price \( M \)
To find \( M \), divide both sides by 0.01:
\[ M = \frac{15}{0.01} = 1500 \]

### Final Answer
The marked price of the watch is ₹1500.

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