While selling a cooler, a shopkeeper gives a discount of 10% on the marked price. If he gives a discount of 12% he earns Rs 35 less as profit. The marked price of the cooler is

Options

A. Rs. 1,650
B. Rs. 1,625
C. Rs. 1,725
D. Rs. 1,750

Answer

To solve the problem step by step, let's denote the marked price of the cooler as \( M \).

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

### Step 2: Calculate the selling price with a 10% discount
When the shopkeeper gives a discount of 10%, the selling price (SP1) can be calculated as:
\[ SP1 = M - (10\% \text{ of } M) = M - 0.1M = 0.9M \]

### Step 3: Calculate the selling price with a 12% discount
When the shopkeeper gives a discount of 12%, the selling price (SP2) can be calculated as:
\[ SP2 = M - (12\% \text{ of } M) = M - 0.12M = 0.88M \]

### Step 4: Set up the profit equations
Let the cost price (CP) of the cooler be \( C \). The profit when selling at SP1 is:
\[ \text{Profit1} = SP1 - C = 0.9M - C \]
The profit when selling at SP2 is:
\[ \text{Profit2} = SP2 - C = 0.88M - C \]

### Step 5: Relate the profits
According to the problem, when a discount of 12% is given, the profit is Rs 35 less than when a discount of 10% is given. Therefore, we can write:
\[ \text{Profit1} - \text{Profit2 = 35} \]
Substituting the profit equations:
\[ (0.9M - C) - (0.88M - C) = 35 \]
This simplifies to:
\[ 0.9M - 0.88M = 35 \]
\[ 0.02M = 35 \]

### Step 6: Solve for the marked price
Now, we can solve for \( M \):
\[ M = \frac{35}{0.02} = 1750 \]

### Conclusion
The marked price of the cooler is \( \text{Rs } 1750 \).

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