What would be the printed price of a watch purchased at Rs. 380 , so that after giving `5%` discout , there is `25%` profit ?

Options

A. Rs . 400
B. Rs . 450
C. Rs . 500
D. Rs . 600

Answer

To find the printed price (marked price) of the watch purchased at Rs. 380, so that after giving a 5% discount, there is a 25% profit, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Cost Price (CP)**:
The cost price of the watch is given as Rs. 380.

2. **Determine the Selling Price (SP) for a 25% Profit**:
To find the selling price that includes a 25% profit, we use the formula:
\[ SP = CP + \left(\frac{25}{100} \times CP\right) \]
Substituting the cost price:
\[ SP = 380 + \left(\frac{25}{100} \times 380\right) = 380 + 95 = 475 \]
So, the selling price should be Rs. 475.

3. **Set Up the Equation for Selling Price with Discount**:
The selling price after a 5% discount on the marked price (MP) is given by:
\[ SP = MP - \left(\frac{5}{100} \times MP\right) \]
This can be rewritten as:
\[ SP = MP \left(1 - \frac{5}{100}\right) = MP \left(\frac{95}{100}\right) \]

4. **Equate the Selling Price to the Expression with Marked Price**:
Now we equate the two expressions for selling price:
\[ 475 = MP \left(\frac{95}{100}\right) \]

5. **Solve for Marked Price (MP)**:
Rearranging the equation to solve for MP:
\[ MP = 475 \times \left(\frac{100}{95}\right) \]
Calculating the right-hand side:
\[ MP = 475 \times \frac{100}{95} = 475 \times \frac{20}{19} = \frac{9500}{19} \approx 500 \]
Therefore, the marked price is Rs. 500.

### Final Answer:
The printed price (marked price) of the watch should be Rs. 500.

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