Aman started a shoes manufacturing company, manufacturing cost of each shoes is Rs. 500, Raw material cost is Rs 300 and transport cost of Rs 100 If company manufactured 150 Shoes in first order and sold `50%` of shoes on half of its cost price., then find on how much percent above of cost price should be remaining shoes sold to gets `50%` profit on total cost?

Options

A. `100%`
B. `150%`
C. `137.5%`
D. `125%`

Answer

To solve the problem step by step, we will break down the information provided and calculate the required values.

### Step 1: Calculate the total cost price of manufacturing 150 shoes.
- **Manufacturing cost per shoe** = Rs. 500
- **Total shoes manufactured** = 150

**Total Cost Price (CP)** = Manufacturing cost per shoe × Total shoes manufactured
**Total CP** = 500 × 150 = Rs. 75,000

**Hint:** Remember to multiply the cost per item by the total number of items to find the total cost.

### Step 2: Calculate the selling price of the first 50% of the shoes.
- **50% of shoes manufactured** = 150 × 50% = 75 shoes
- **Selling price per shoe on half of its cost price** = Rs. 500 / 2 = Rs. 250

**Total Selling Price (SP) for 75 shoes** = Selling price per shoe × Number of shoes sold
**Total SP** = 250 × 75 = Rs. 18,750

**Hint:** When selling at a discount, divide the original price by 2 to find the new selling price.

### Step 3: Calculate the total selling price required for a 50% profit.
- **Desired profit** = 50% of Total CP
- **Total profit required** = 75,000 × 50% = Rs. 37,500

**Total Selling Price required for 50% profit** = Total CP + Total profit required
**Total SP required** = 75,000 + 37,500 = Rs. 112,500

**Hint:** To find the total selling price needed for a desired profit, add the profit to the total cost price.

### Step 4: Calculate the remaining amount needed from the second batch of shoes.
**Remaining amount needed** = Total SP required - Total SP from first batch
**Remaining amount** = 112,500 - 18,750 = Rs. 93,750

**Hint:** Subtract the amount already earned from the total amount needed to find out what is still required.

### Step 5: Calculate the selling price per shoe for the remaining shoes.
- **Remaining shoes** = 150 - 75 = 75 shoes

**Selling Price per shoe for remaining shoes** = Remaining amount needed / Remaining shoes
**Selling Price per shoe** = 93,750 / 75 = Rs. 1,250

**Hint:** To find the price per item, divide the total amount needed by the number of items left.

### Step 6: Calculate the percentage increase above the cost price.
- **Cost price per shoe** = Rs. 500
- **Selling price per shoe** = Rs. 1,250

**Increase in price** = Selling price - Cost price
**Increase** = 1,250 - 500 = Rs. 750

**Percentage increase** = (Increase / Cost price) × 100
**Percentage increase** = (750 / 500) × 100 = 150%

**Hint:** To find the percentage increase, subtract the original price from the new price, divide by the original price, and multiply by 100.

### Final Answer:
The remaining shoes should be sold at **150%** above the cost price to achieve a 50% profit on the total cost.