The raw material and manufacturing cost formed individually 70% and 30% of the total cost and the profit percentage is 14.28% of the raw material. If the cost of raw material increase by 20% and the cost of manufacturing is increased by 40% and the selling price is increased by 80%, then the new profit percentage is :

Options

A. 0.57
B. `65.8%`
C. `60%`
D. Cannot be determined

Answer

To solve the problem step by step, let's break it down clearly.

### Step 1: Define the Costs
Let the total cost be represented as 100 units (this simplifies calculations). According to the problem:
- Cost of raw material = 70% of total cost = 70 units
- Cost of manufacturing = 30% of total cost = 30 units

### Step 2: Calculate the Initial Profit
The profit percentage is given as 14.28% of the raw material cost.
- Profit = 14.28% of 70 = (14.28/100) * 70 = 10 units
- Selling Price (SP) = Total Cost + Profit = 100 + 10 = 110 units

### Step 3: Adjust the Costs for Increases
Now, we will adjust the costs based on the given percentage increases:
- New cost of raw material = 70 + (20% of 70) = 70 + (0.20 * 70) = 70 + 14 = 84 units
- New cost of manufacturing = 30 + (40% of 30) = 30 + (0.40 * 30) = 30 + 12 = 42 units

### Step 4: Calculate the New Total Cost
- New Total Cost = New cost of raw material + New cost of manufacturing = 84 + 42 = 126 units

### Step 5: Adjust the Selling Price
The selling price is increased by 80%:
- New Selling Price = Old Selling Price + (80% of Old Selling Price) = 110 + (0.80 * 110) = 110 + 88 = 198 units

### Step 6: Calculate the New Profit
- New Profit = New Selling Price - New Total Cost = 198 - 126 = 72 units

### Step 7: Calculate the New Profit Percentage
- New Profit Percentage = (New Profit / New Total Cost) * 100 = (72 / 126) * 100

Calculating this gives:
- New Profit Percentage = (72 / 126) * 100 = 57.14%

### Final Answer
The new profit percentage is **57.14%**.

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