A grinder was marked at ₹ 3,600. After giving a discount of 10 % the dealer made a profit of 8 %. Calculate the cost price.

Options

A. ₹ 3,000
B. ₹ 3,312
C. ₹ 3,240
D. ₹ 2,960

Answer

To find the cost price of the grinder, we can follow these steps:

### Step 1: Calculate the Selling Price after Discount
The marked price of the grinder is ₹3,600, and a discount of 10% is given.

\[ \text{Discount} = \frac{10}{100} \times 3600 = 360 \]

Now, subtract the discount from the marked price to find the selling price.

\[ \text{Selling Price} = \text{Marked Price} - \text{Discount} = 3600 - 360 = 3240 \]

### Step 2: Relate Selling Price to Cost Price
The dealer makes a profit of 8% on the cost price (CP). This means the selling price is 108% of the cost price.

\[ \text{Selling Price} = \frac{108}{100} \times \text{CP} \]

Substituting the selling price we calculated:

\[ 3240 = \frac{108}{100} \times \text{CP} \]

### Step 3: Solve for Cost Price
To find the cost price, rearrange the equation:

\[ \text{CP} = \frac{3240 \times 100}{108} \]

Now, calculate it step by step:

1. Multiply 3240 by 100:

\[ 3240 \times 100 = 324000 \]

2. Now divide by 108:

\[ \text{CP} = \frac{324000}{108} \]

To simplify, divide both the numerator and denominator by 36:

\[ \text{CP} = \frac{324000 \div 36}{108 \div 36} = \frac{9000}{3} = 3000 \]

Thus, the cost price of the grinder is ₹3,000.

### Final Answer
The cost price of the grinder is ₹3,000.

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