Rani bought a bag with 30% discount on the listed price. Had she not got the discount, she would have paid Rs 82.5 extra. At what price did she buy the bag?

Options

A. Rs. 192.5
B. Rs. 275
C. Rs. 117.85
D. CND

Answer

To find out at what price Rani bought the bag, we can follow these steps:

### Step 1: Define the listed price
Let the listed price of the bag be denoted as \( P \).

### Step 2: Calculate the discount
Rani received a discount of 30% on the listed price. Therefore, the amount of discount can be calculated as:
\[ \text{Discount} = 30\% \text{ of } P = \frac{30}{100} \times P = 0.3P \]

### Step 3: Calculate the selling price after discount
The selling price (the price Rani actually paid) after applying the discount is:
\[ \text{Selling Price} = P - \text{Discount} = P - 0.3P = 0.7P \]

### Step 4: Relate the selling price to the extra amount paid without discount
According to the question, if Rani had not received the discount, she would have paid Rs 82.5 extra. This means:
\[ P = \text{Selling Price} + 82.5 \]
Substituting the selling price from Step 3:
\[ P = 0.7P + 82.5 \]

### Step 5: Solve for \( P \)
To isolate \( P \), we can rearrange the equation:
\[ P - 0.7P = 82.5 \]
\[ 0.3P = 82.5 \]
Now, divide both sides by 0.3:
\[ P = \frac{82.5}{0.3} = 275 \]

### Step 6: Calculate the selling price (price Rani bought the bag for)
Now that we have the listed price \( P \), we can find the selling price:
\[ \text{Selling Price} = 0.7P = 0.7 \times 275 = 192.5 \]

### Conclusion
Rani bought the bag for Rs 192.5.

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