A shopkeeper sells a cooler at a discount of 15% If he gives a discount of 19% then he earns Rs. 332 less. What will be the marked price of the cooler?

Options

A. Rs. 8100
B. Rs. 8300
C. Rs. 8700
D. Rs. 8200

Answer

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

### Step 1: Define the discounts
The shopkeeper sells the cooler at a discount of 15%. Therefore, the selling price (SP) after a 15% discount can be calculated as:
\[ SP_{15} = M - 0.15M = 0.85M \]

When the shopkeeper gives a discount of 19%, the selling price becomes:
\[ SP_{19} = M - 0.19M = 0.81M \]

### Step 2: Set up the equation based on the problem statement
According to the problem, the difference in earnings when selling at a 15% discount and a 19% discount is Rs. 332. Therefore, we can write the equation:
\[ SP_{15} - SP_{19} = 332 \]
Substituting the expressions for \( SP_{15} \) and \( SP_{19} \):
\[ 0.85M - 0.81M = 332 \]

### Step 3: Simplify the equation
Now, simplify the left side of the equation:
\[ 0.04M = 332 \]

### Step 4: Solve for \( M \)
To find \( M \), divide both sides by 0.04:
\[ M = \frac{332}{0.04} \]
Calculating the right side:
\[ M = 8300 \]

### Conclusion
The marked price of the cooler is Rs. 8300.