Pratap bought a radio with `25%` discount on the original price. He got Rs. 40 more than the original price by selling it at `140%` of the price at which the bought. At what price did he buy the ratio?

Options

A. Rs. 600
B. Rs. 700
C. Rs. 800
D. Rs. 900

Answer

To find the price at which Pratap bought the radio, let's break down the problem step by step.

### Step 1: Define the Original Price
Let the original price of the radio be \( x \).

### Step 2: Calculate the Buying Price After Discount
Pratap bought the radio with a 25% discount. Therefore, the price he paid (buying price) is:
\[ \text{Buying Price} = x - 0.25x = 0.75x \]

### Step 3: Determine the Selling Price
According to the problem, Pratap sold the radio at 140% of the price he bought it for. Hence, the selling price is:
\[ \text{Selling Price} = 1.4 \times (0.75x) = 1.05x \]

### Step 4: Relate Selling Price to Original Price
The problem states that he got Rs. 40 more than the original price by selling it. Therefore, we can set up the equation:
\[ 1.05x = x + 40 \]

### Step 5: Solve for \( x \)
Now, we will solve the equation:
\[ 1.05x - x = 40 \]
\[ 0.05x = 40 \]
\[ x = \frac{40}{0.05} = 800 \]

### Step 6: Calculate the Buying Price
Now that we have the original price \( x = 800 \), we can find the buying price:
\[ \text{Buying Price} = 0.75x = 0.75 \times 800 = 600 \]

### Final Answer
Pratap bought the radio for Rs. 600.

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