While selling a shirt, a shopkeeper gives a discount of 7%. If he had given a discount of 9%, he would have got Rs. 15 less as profit. The marked price of the shirt is

Options

A. Rs.750
B. Rs.720
C. Rs.712.50
D. Rs.600

Answer

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

### Step 1: Define Variables
Let the marked price of the shirt be \( M \).

**Hint:** Start by identifying what you need to find and define your variables clearly.

### Step 2: Calculate Selling Prices
1. When a discount of 7% is given, the selling price (SP1) can be calculated as:
\[ SP1 = M - 0.07M = 0.93M \]
This means the selling price after a 7% discount is 93% of the marked price.

2. When a discount of 9% is given, the selling price (SP2) can be calculated as:
\[ SP2 = M - 0.09M = 0.91M \]
This means the selling price after a 9% discount is 91% of the marked price.

**Hint:** Use the formula for selling price after applying a discount: \( SP = M - (Discount \times M) \).

### Step 3: Set Up the Profit Difference Equation
According to the problem, if the shopkeeper gives a discount of 9%, he would earn Rs. 15 less profit than when he gives a discount of 7%. Therefore, we can set up the equation:
\[ SP1 - SP2 = 15 \]
Substituting the expressions for SP1 and SP2:
\[ 0.93M - 0.91M = 15 \]

**Hint:** Relate the selling prices to the profit difference stated in the problem.

### Step 4: Simplify the Equation
Now, simplify the equation:
\[ 0.02M = 15 \]

**Hint:** Combine like terms to isolate the variable.

### Step 5: Solve for M
To find \( M \), divide both sides by 0.02:
\[ M = \frac{15}{0.02} = 750 \]

**Hint:** When solving for a variable, ensure you perform the same operation on both sides of the equation.

### Conclusion
The marked price of the shirt is Rs. 750.

**Final Answer:** The marked price of the shirt is Rs. 750.

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