A man sells two horse for Rs. 4000 each, neither losing nor gaining in the deal. If he sold one horse at a gain of `25%` the other horse is sold at a loss of-

Options

A. `(16)2/3%`
B. `(18)2/9%`
C. `25%`
D. None of these

Answer

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

### Step 1: Understand the Selling Price (SP)
The man sells two horses for Rs. 4000 each. Therefore, the Selling Price (SP) of each horse is:
- SP of Horse 1 = Rs. 4000
- SP of Horse 2 = Rs. 4000

### Step 2: Calculate the Cost Price (CP) of the First Horse
The first horse is sold at a gain of 25%. To find the Cost Price (CP) of the first horse, we use the formula:
\[ CP = \frac{SP \times 100}{100 + \text{Profit Percent}} \]
Substituting the values:
\[ CP_1 = \frac{4000 \times 100}{100 + 25} = \frac{4000 \times 100}{125} = \frac{400000}{125} = 3200 \]
So, the Cost Price of the first horse is Rs. 3200.

### Step 3: Calculate the Total Cost Price of Both Horses
Since the man neither gains nor loses in the overall deal, the total Selling Price of both horses equals the total Cost Price of both horses.
\[ \text{Total SP} = 4000 + 4000 = 8000 \]
Thus, the total Cost Price (CP) of both horses is also Rs. 8000.

### Step 4: Calculate the Cost Price of the Second Horse
Now, we can find the Cost Price of the second horse using the total CP:
\[ CP_2 = \text{Total CP} - CP_1 = 8000 - 3200 = 4800 \]
So, the Cost Price of the second horse is Rs. 4800.

### Step 5: Calculate the Loss on the Second Horse
The Selling Price of the second horse is Rs. 4000. To find the loss incurred on the second horse, we use the formula:
\[ \text{Loss} = CP - SP \]
Substituting the values:
\[ \text{Loss} = 4800 - 4000 = 800 \]

### Step 6: Calculate the Loss Percentage
To find the loss percentage, we use the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{CP}\right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left(\frac{800}{4800}\right) \times 100 = \frac{80000}{4800} \approx 16.67\% \]

### Final Answer
The loss on the second horse is approximately **16.67%**.

---