By selling 144 hens Mahesh suffered a loss equal to the selling price of 6 hens. His loss percent is

Options

A. 0.04
B. 0.03
C. 0.09
D. 4 `1/2` %

Answer

To find the loss percentage Mahesh incurred from selling 144 hens, we can follow these steps:

### Step 1: Define Variables
Let the cost price (CP) of 1 hen be \( x \).
Let the selling price (SP) of 1 hen be \( y \).

### Step 2: Calculate Total Cost Price
The total cost price for 144 hens can be calculated as:
\[ \text{Total CP} = 144 \times x \]

### Step 3: Calculate Total Selling Price
The total selling price for 144 hens is:
\[ \text{Total SP} = 144 \times y \]

### Step 4: Determine Loss
According to the problem, Mahesh suffered a loss equal to the selling price of 6 hens. Therefore, the loss can be expressed as:
\[ \text{Loss} = 6 \times y \]

### Step 5: Relate Loss to Cost Price and Selling Price
The loss can also be calculated as the difference between the total cost price and the total selling price:
\[ \text{Loss} = \text{Total CP} - \text{Total SP} \]
Substituting the values we calculated:
\[ 6y = 144x - 144y \]

### Step 6: Rearranging the Equation
Rearranging the equation gives:
\[ 144y + 6y = 144x \]
\[ 150y = 144x \]

### Step 7: Calculate Selling Price in Terms of Cost Price
From the equation \( 150y = 144x \), we can express \( y \) in terms of \( x \):
\[ y = \frac{144}{150} x = \frac{24}{25} x \]

### Step 8: Calculate Loss
Now we can find the loss:
\[ \text{Loss} = \text{Total CP} - \text{Total SP} = 144x - 144y \]
Substituting \( y \):
\[ \text{Loss} = 144x - 144 \left(\frac{24}{25} x\right) \]
\[ = 144x - \frac{3456}{25} x \]
\[ = 144x - 138.24x = 5.76x \]

### Step 9: Calculate Loss Percentage
The loss percentage is given by the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{\text{Total CP}}\right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left(\frac{5.76x}{144x}\right) \times 100 \]
\[ = \left(\frac{5.76}{144}\right) \times 100 \]
\[ = 4\% \]

### Final Answer
Thus, Mahesh's loss percentage is **4%**.

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