Directions : These questions are based on the information given below:
In manufacturing a certain item, 40% of the expenditure is on account of raw materials 20% on account of labour charges, 20% on account to fixed charges and the rest on miscellaneous. The item is solid at a profit of 25%. The price of the raw materials went up by 15% and the labour charges went up by 20% and the cost on the miscellaneous heads went up by 50% while the fixed costs remained unchanged.
If the selling price remained unchanged, then what is the new profit percentage ?

Options

A. `2%`
B. `4%`
C. `4(1)/(6)%`
D. `10%`

Answer

To solve the problem step by step, we will break down the information given and calculate the new profit percentage after the increase in costs.

### Step 1: Determine the initial costs
Let's assume the total manufacturing cost of the item is 100 units (this simplifies our calculations).

- Raw materials: 40% of 100 = 40 units
- Labour charges: 20% of 100 = 20 units
- Fixed charges: 20% of 100 = 20 units
- Miscellaneous costs: 100 - (40 + 20 + 20) = 20 units

### Step 2: Calculate the selling price
The item is sold at a profit of 25%. Therefore, the selling price (SP) can be calculated as follows:

\[ SP = CP + (25\% \text{ of } CP) = 100 + 25 = 125 \text{ units} \]

### Step 3: Calculate the new costs after the price increases
Now, we need to calculate the new costs after the increases:

- **Raw materials**: Increased by 15%
\[ \text{New Raw Material Cost} = 40 + (15\% \text{ of } 40) = 40 + 6 = 46 \text{ units} \]

- **Labour charges**: Increased by 20%
\[ \text{New Labour Cost} = 20 + (20\% \text{ of } 20) = 20 + 4 = 24 \text{ units} \]

- **Fixed charges**: Remain unchanged
\[ \text{New Fixed Cost} = 20 \text{ units} \]

- **Miscellaneous costs**: Increased by 50%
\[ \text{New Miscellaneous Cost} = 20 + (50\% \text{ of } 20) = 20 + 10 = 30 \text{ units} \]

### Step 4: Calculate the total new cost
Now, we sum up all the new costs:

\[ \text{Total New Cost} = 46 + 24 + 20 + 30 = 120 \text{ units} \]

### Step 5: Calculate the new profit
The profit can be calculated as:

\[ \text{Profit} = SP - \text{Total New Cost} = 125 - 120 = 5 \text{ units} \]

### Step 6: Calculate the new profit percentage
The new profit percentage can be calculated using the formula:

\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Total New Cost}}\right) \times 100 \]

Substituting the values:

\[ \text{Profit Percentage} = \left(\frac{5}{120}\right) \times 100 = \frac{500}{120} \approx 4.17\% \]

### Final Answer
The new profit percentage is approximately **4.17%**.

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