After allowing 10% discount , a dealer wishes to sell a machine for Rs. 2,700. At what price must the machine be marked ?

Options

A. Rs. 270
B. Rs. 3,000
C. Rs. 2,970
D. Rs. 2,430

Answer

To find the marked price of the machine, we can follow these steps:

### Step 1: Understand the relationship between Selling Price, Marked Price, and Discount
The relationship can be expressed as:
\[ \text{Selling Price (SP)} = \text{Marked Price (MP)} - \text{Discount} \]

### Step 2: Express the Discount in terms of Marked Price
Given that the discount is 10%, we can express the discount as:
\[ \text{Discount} = 10\% \text{ of Marked Price} = \frac{10}{100} \times \text{MP} = 0.1 \times \text{MP} \]

### Step 3: Substitute the Discount into the Selling Price equation
Now, we can substitute the discount into the Selling Price equation:
\[ \text{SP} = \text{MP} - 0.1 \times \text{MP} \]
This simplifies to:
\[ \text{SP} = 0.9 \times \text{MP} \]

### Step 4: Set up the equation with the given Selling Price
We know from the question that the Selling Price (SP) is Rs. 2700. Therefore, we can write:
\[ 2700 = 0.9 \times \text{MP} \]

### Step 5: Solve for Marked Price (MP)
To find the Marked Price, we can rearrange the equation:
\[ \text{MP} = \frac{2700}{0.9} \]

### Step 6: Calculate the Marked Price
Now, perform the calculation:
\[ \text{MP} = \frac{2700}{0.9} = 3000 \]

### Conclusion
Thus, the marked price of the machine must be Rs. 3000.

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