On a television of brand A the discount is 25% and on television of brand B the discount is 40% The price of B after discount Rs 2,250 greater than the price of A after discount. Whatis the marked price of A (in Rs) if marked price of B is Rs 35,000?

Options

A. 18750
B. 21000
C. 25000
D. 17850

Answer

To solve the problem step by step, we will determine the marked price of television brand A based on the information provided.

### Step 1: Identify the given information
- Discount on brand A = 25%
- Discount on brand B = 40%
- Marked price of brand B = Rs 35,000
- Selling price of brand B is Rs 2,250 greater than the selling price of brand A.

### Step 2: Calculate the selling price of brand B
The selling price (SP) after a discount can be calculated using the formula:
\[ \text{SP} = \text{Marked Price} - \text{Discount} \]
For brand B:
- Discount on brand B = 40% of Rs 35,000
\[ \text{Discount} = 0.40 \times 35000 = 14000 \]
Thus, the selling price of brand B is:
\[ \text{SP}_B = 35000 - 14000 = 21000 \]

### Step 3: Set up the equation for selling price of brand A
Let the selling price of brand A be \( \text{SP}_A \). According to the problem, we know:
\[ \text{SP}_B = \text{SP}_A + 2250 \]
Substituting the value of \( \text{SP}_B \):
\[ 21000 = \text{SP}_A + 2250 \]

### Step 4: Solve for the selling price of brand A
Rearranging the equation gives:
\[ \text{SP}_A = 21000 - 2250 \]
\[ \text{SP}_A = 18750 \]

### Step 5: Calculate the marked price of brand A
Now we need to find the marked price of brand A. Since the discount on brand A is 25%, we can use the formula:
\[ \text{SP}_A = \text{MP}_A - \text{Discount on MP}_A \]
The discount on brand A can be expressed as:
\[ \text{Discount on MP}_A = 0.25 \times \text{MP}_A \]
Thus, we can write:
\[ 18750 = \text{MP}_A - 0.25 \times \text{MP}_A \]
This simplifies to:
\[ 18750 = 0.75 \times \text{MP}_A \]

### Step 6: Solve for the marked price of brand A
To find \( \text{MP}_A \):
\[ \text{MP}_A = \frac{18750}{0.75} \]
\[ \text{MP}_A = 25000 \]

### Final Answer
The marked price of brand A is Rs 25,000.

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