If the discount of a book is 30% of the SP and discount % equals profit %, then find the ratio of discount offered to the CP.

Options

A. `17:52`
B. `24:65`
C. `28:55`
D. `32:85`

Answer

To solve the problem step by step, we will follow the information given in the question and the video transcript.

### Step 1: Understand the Given Information
We know that:
- The discount on the book is 30% of the Selling Price (SP).
- The discount percentage equals the profit percentage.

### Step 2: Assume the Selling Price
Let's assume the Selling Price (SP) of the book is ₹100. This simplifies our calculations.

### Step 3: Calculate the Discount
The discount is 30% of the Selling Price:
\[ \text{Discount} = 30\% \text{ of } 100 = \frac{30}{100} \times 100 = ₹30 \]

### Step 4: Calculate the Market Price
The Market Price (MP) is the sum of the Selling Price and the Discount:
\[ \text{Market Price} = \text{Selling Price} + \text{Discount} = 100 + 30 = ₹130 \]

### Step 5: Calculate the Discount Percentage
Now, we can calculate the discount percentage based on the Market Price:
\[ \text{Discount Percentage} = \left(\frac{\text{Discount}}{\text{Market Price}}\right) \times 100 = \left(\frac{30}{130}\right) \times 100 \]
Calculating this gives:
\[ \text{Discount Percentage} = \frac{30 \times 100}{130} = \frac{3000}{130} \approx 23.07\% \]

### Step 6: Set Profit Percentage Equal to Discount Percentage
Since the problem states that the discount percentage equals the profit percentage, we have:
\[ \text{Profit Percentage} = 23.07\% \]

### Step 7: Calculate the Cost Price (CP)
Using the Selling Price and the Profit Percentage, we can find the Cost Price:
\[ \text{Selling Price} = \text{Cost Price} + \text{Profit} \]
Where Profit is given by:
\[ \text{Profit} = \left(\frac{\text{Profit Percentage}}{100}\right) \times \text{Cost Price} \]
Let the Cost Price be \( CP \):
\[ 100 = CP + \left(\frac{23.07}{100} \times CP\right) \]
This simplifies to:
\[ 100 = CP \left(1 + \frac{23.07}{100}\right) = CP \left(\frac{123.07}{100}\right) \]
Now, solving for \( CP \):
\[ CP = \frac{100 \times 100}{123.07} \approx ₹81.25 \]

### Step 8: Find the Ratio of Discount to Cost Price
Finally, we find the ratio of the Discount to the Cost Price:
\[ \text{Ratio} = \frac{\text{Discount}}{\text{Cost Price}} = \frac{30}{81.25} \]
Calculating this gives:
\[ \text{Ratio} \approx 0.3692 \]

### Conclusion
Thus, the ratio of the discount offered to the cost price is approximately \( 0.3692 \).

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