A shopkeeper allows 20% discount on his advertised price and to make a profit of 25% on his outlay. What is the advertised price (in Rs.) on which he gains Rs 6000 ?

Options

A. a)36000
B. b)37500
C. c)39000
D. d)42500

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript:

### Step 1: Understand the Profit and Cost Price
The shopkeeper makes a profit of Rs. 6000, which is 25% of the cost price (CP). We can set up the equation:
\[ \text{Profit} = \text{CP} \times \frac{25}{100} \]
Given that the profit is Rs. 6000, we can write:
\[ 6000 = \text{CP} \times \frac{25}{100} \]

**Hint:** Remember that profit percentage is always calculated based on the cost price.

### Step 2: Calculate the Cost Price
To find the cost price (CP), we rearrange the equation:
\[ \text{CP} = \frac{6000 \times 100}{25} \]
Calculating this gives:
\[ \text{CP} = \frac{600000}{25} = 24000 \]

**Hint:** To isolate CP, multiply both sides by 100 and then divide by 25.

### Step 3: Calculate the Selling Price
The selling price (SP) is the cost price plus the profit:
\[ \text{SP} = \text{CP} + \text{Profit} = 24000 + 6000 = 30000 \]

**Hint:** Selling price can be found by adding the profit to the cost price.

### Step 4: Relate Selling Price to Advertised Price
The shopkeeper offers a 20% discount on the advertised price (AP). The relationship between the selling price and the advertised price is given by:
\[ \text{SP} = \text{AP} \times \left(1 - \frac{20}{100}\right) = \text{AP} \times 0.8 \]
Substituting the selling price we found:
\[ 30000 = \text{AP} \times 0.8 \]

**Hint:** The selling price is 80% of the advertised price due to the discount.

### Step 5: Calculate the Advertised Price
To find the advertised price (AP), we rearrange the equation:
\[ \text{AP} = \frac{30000}{0.8} \]
Calculating this gives:
\[ \text{AP} = \frac{30000 \times 100}{80} = 37500 \]

**Hint:** To isolate AP, divide the selling price by 0.8.

### Conclusion
The advertised price on which the shopkeeper gains Rs. 6000 is Rs. 37,500.

**Final Answer:** Rs. 37,500