Amit received a discount of 20 % on an item which was sold at Rs. 1600. What was the marked price of the item?

Options

A. Rs. 2000
B. Rs. 1680
C. Rs. 2200
D. Rs. 1280

Answer

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

### Step 1: Understand the relationship between Selling Price, Marked Price, and Discount
The relationship can be expressed as:
\[ \text{Selling Price} = \text{Marked Price} - \text{Discount} \]
Where:
- Selling Price (SP) = Rs. 1600
- Discount = 20% of Marked Price (MP)

### Step 2: Express the Discount in terms of Marked Price
Since the discount is 20% of the marked price, we can write:
\[ \text{Discount} = \frac{20}{100} \times \text{Marked Price} = 0.2 \times \text{Marked Price} \]

### Step 3: Substitute the Discount into the Selling Price equation
Now, substituting the discount in the Selling Price equation, we get:
\[ 1600 = \text{Marked Price} - (0.2 \times \text{Marked Price}) \]

### Step 4: Simplify the equation
This can be simplified to:
\[ 1600 = \text{Marked Price} (1 - 0.2) \]
\[ 1600 = \text{Marked Price} \times 0.8 \]

### Step 5: Solve for Marked Price
To find the marked price, we can rearrange the equation:
\[ \text{Marked Price} = \frac{1600}{0.8} \]
Calculating this gives:
\[ \text{Marked Price} = 2000 \]

### Conclusion
Thus, the marked price of the item is Rs. 2000.

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