A man sells two cows for ₹ 4000 each, neither losing nor gaining in the deal. If he sells one cow at a gain of 28%, them the other cow is sold at a loss of …………….

Answer

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

### Step 1: Understand the Selling Price of Both Cows
The man sells two cows for ₹4000 each. Therefore, the total selling price (SP) for both cows is:
\[ \text{Total SP} = 4000 + 4000 = ₹8000 \]

### Step 2: Calculate the Selling Price of One Cow
The selling price of one cow is:
\[ \text{SP of one cow} = ₹4000 \]

### Step 3: Determine the Gain on One Cow
One cow is sold at a gain of 28%. To find the cost price (CP) of this cow, we can use the formula:
\[ \text{SP} = \text{CP} + \text{Gain} \]
Where Gain can be expressed as:
\[ \text{Gain} = \frac{28}{100} \times \text{CP} \]
Thus, we can rewrite the equation as:
\[ 4000 = \text{CP} + \left(\frac{28}{100} \times \text{CP}\right) \]
This simplifies to:
\[ 4000 = \text{CP} \left(1 + \frac{28}{100}\right) \]
\[ 4000 = \text{CP} \left(\frac{128}{100}\right) \]
Now, solving for CP:
\[ \text{CP} = 4000 \times \frac{100}{128} \]
\[ \text{CP} = 4000 \times 0.78125 = ₹3125 \]

### Step 4: Calculate the Cost Price of the Second Cow
Since there is no overall gain or loss in the transaction, the total cost price of both cows must equal the total selling price of both cows:
\[ \text{Total CP} = \text{CP of first cow} + \text{CP of second cow} \]
Let the cost price of the second cow be \( x \):
\[ 3125 + x = 8000 \]
Solving for \( x \):
\[ x = 8000 - 3125 = ₹4875 \]

### Step 5: Calculate the Loss on the Second Cow
The selling price of the second cow is ₹4000. The cost price of the second cow is ₹4875. To find the loss:
\[ \text{Loss} = \text{CP of second cow} - \text{SP of second cow} \]
\[ \text{Loss} = 4875 - 4000 = ₹875 \]

### Step 6: Calculate the Loss Percentage
The loss percentage can be calculated using the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{\text{CP of second cow}}\right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left(\frac{875}{4875}\right) \times 100 \]
Calculating this gives:
\[ \text{Loss Percentage} = 17.94\% \]

### Final Answer
The other cow is sold at a loss of **17.94%**.

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