Rita bought a television set with 20% discount on the labelled price. She made a profit of 800 by selling it for 16,800. The labelled price of the set was

Options

A. 18000
B. 20000
C. 20800
D. 24000

Answer

To solve the problem step by step, we need to find the labelled price (also known as the marked price) of the television set that Rita bought.

### Step 1: Understand the given information
- Rita bought a television set at a 20% discount on the labelled price.
- She sold the television set for ₹16,800.
- Rita made a profit of ₹800.

### Step 2: Determine the cost price (CP) of the television set
Since Rita made a profit of ₹800 when selling the television for ₹16,800, we can find the cost price (CP) using the formula:
\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]
Substituting the known values:
\[ 16,800 = \text{CP} + 800 \]
To find CP, we rearrange the equation:
\[ \text{CP} = 16,800 - 800 \]
\[ \text{CP} = 16,000 \]

### Step 3: Relate the cost price to the labelled price
Rita bought the television set at a 20% discount on the labelled price (let's denote the labelled price as \( X \)). This means she paid 80% of the labelled price:
\[ \text{CP} = 80\% \text{ of } X \]
This can be expressed mathematically as:
\[ \text{CP} = 0.8X \]

### Step 4: Substitute the cost price into the equation
Now we can substitute the value of CP we found in Step 2 into the equation:
\[ 16,000 = 0.8X \]

### Step 5: Solve for the labelled price (X)
To find \( X \), we can rearrange the equation:
\[ X = \frac{16,000}{0.8} \]
Calculating this gives:
\[ X = 20,000 \]

### Conclusion
The labelled price of the television set is ₹20,000.

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