A person sold two cows each for ₹ 9900. If he gained `10%` on. one and lost `20%` on the other, then which of the following is true?

Options

A. He gained ₹ 200
B. He'lost ₹ 200
C. He neither gained nor lost
D. None of the above

Answer

To solve the problem step by step, we need to calculate the cost price of each cow based on the selling price and the profit/loss percentages.

### Step 1: Calculate the Cost Price of the First Cow
The first cow is sold at a profit of 10%. Let the cost price of the first cow be \( CP_1 \).

Given:
- Selling Price (SP) of the first cow = ₹ 9900
- Profit = 10%

Using the formula for selling price:
\[ SP = CP + \text{Profit} \]
We can express the profit in terms of cost price:
\[ \text{Profit} = \frac{10}{100} \times CP_1 = 0.1 \times CP_1 \]
Thus, we can rewrite the selling price equation as:
\[ 9900 = CP_1 + 0.1 \times CP_1 \]
\[ 9900 = 1.1 \times CP_1 \]
Now, we can solve for \( CP_1 \):
\[ CP_1 = \frac{9900}{1.1} = 9000 \]

### Step 2: Calculate the Cost Price of the Second Cow
The second cow is sold at a loss of 20%. Let the cost price of the second cow be \( CP_2 \).

Given:
- Selling Price (SP) of the second cow = ₹ 9900
- Loss = 20%

Using the formula for selling price:
\[ SP = CP - \text{Loss} \]
We can express the loss in terms of cost price:
\[ \text{Loss} = \frac{20}{100} \times CP_2 = 0.2 \times CP_2 \]
Thus, we can rewrite the selling price equation as:
\[ 9900 = CP_2 - 0.2 \times CP_2 \]
\[ 9900 = 0.8 \times CP_2 \]
Now, we can solve for \( CP_2 \):
\[ CP_2 = \frac{9900}{0.8} = 12375 \]

### Step 3: Calculate Total Cost Price and Total Selling Price
Now we can calculate the total cost price and total selling price of both cows.

Total Cost Price (CP) = \( CP_1 + CP_2 = 9000 + 12375 = 21375 \)

Total Selling Price (SP) = \( 9900 + 9900 = 19800 \)

### Step 4: Calculate Overall Profit or Loss
Now we can determine if there was an overall profit or loss:
\[ \text{Total Profit or Loss} = \text{Total Selling Price} - \text{Total Cost Price} \]
\[ \text{Total Profit or Loss} = 19800 - 21375 = -1575 \]

Since the result is negative, it indicates a loss.

### Conclusion
The person incurred a loss of ₹ 1575.

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