A manufacturer makes a profit of 15% by selling a colour TV for Rs. 5750. If the cost of manufacturing increases by 30% and the price paid by the retailer is increased by 20%, find the profit percent made by the manufacturer.

Options

A. `6 ( 2//13)%`
B. `4 ( 8//13)%`
C. `6 ( 1//13)%`
D. `7 ( 4//13)%`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Original Cost Price (CP)
The selling price (SP) of the color TV is Rs. 5750, and the manufacturer makes a profit of 15%.

To find the cost price (CP), we can use the formula:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where Profit can be expressed as:
\[ \text{Profit} = \frac{\text{Profit \%}}{100} \times \text{CP} \]

Given that the profit percentage is 15%, we can express the selling price as:
\[ \text{SP} = \text{CP} + 0.15 \times \text{CP} = 1.15 \times \text{CP} \]

Now substituting the SP:
\[ 5750 = 1.15 \times \text{CP} \]

To find CP, we rearrange the equation:
\[ \text{CP} = \frac{5750}{1.15} = 5000 \]

### Step 2: Calculate the New Cost Price after Increase
The cost of manufacturing increases by 30%. Therefore, the new cost price (CP_new) can be calculated as:
\[ \text{CP_new} = \text{CP} \times (1 + \text{Increase \%}) = 5000 \times (1 + 0.30) = 5000 \times 1.30 = 6500 \]

### Step 3: Calculate the New Selling Price after Retailer Price Increase
The price paid by the retailer increases by 20%. Therefore, the new selling price (SP_new) can be calculated as:
\[ \text{SP_new} = \text{SP} \times (1 + \text{Increase \%}) = 5750 \times (1 + 0.20) = 5750 \times 1.20 = 6900 \]

### Step 4: Calculate the New Profit
Now we can find the new profit by subtracting the new cost price from the new selling price:
\[ \text{Profit} = \text{SP_new} - \text{CP_new} = 6900 - 6500 = 400 \]

### Step 5: Calculate the New Profit Percentage
Finally, we calculate the profit percentage using the formula:
\[ \text{Profit \%} = \left( \frac{\text{Profit}}{\text{CP_new}} \right) \times 100 = \left( \frac{400}{6500} \right) \times 100 \]
Calculating this gives:
\[ \text{Profit \%} = \frac{400 \times 100}{6500} = \frac{40000}{6500} \approx 6.15\% \]

Thus, the profit percentage made by the manufacturer after the increases is approximately **6.15%**.

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