A person sold two cows each for Rs. 9900. If he gained 10% on one and lost 20% on the other, find the overall loss or profit.

Options

A. He gained Rs. 200
B. He lost Rs. 200
C. He neither gained nor lost
D. none of the above

Answer

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

### Step 1: Determine the Selling Price (SP) of each cow
The selling price of each cow is given as Rs. 9900.

### Step 2: Calculate the Cost Price (CP) of the first cow
For the first cow, there is a gain of 10%. We can use the formula for selling price when there is a profit:

\[ SP = CP + \text{Profit} \]

Since profit is 10% of CP, we can express it as:

\[ SP = CP + 0.10 \times CP = 1.10 \times CP \]

Now, substituting the selling price:

\[ 9900 = 1.10 \times CP_1 \]

To find \(CP_1\):

\[ CP_1 = \frac{9900}{1.10} = 9000 \]

### Step 3: Calculate the Cost Price (CP) of the second cow
For the second cow, there is a loss of 20%. We can use the formula for selling price when there is a loss:

\[ SP = CP - \text{Loss} \]

Since loss is 20% of CP, we can express it as:

\[ SP = CP - 0.20 \times CP = 0.80 \times CP \]

Now, substituting the selling price:

\[ 9900 = 0.80 \times CP_2 \]

To find \(CP_2\):

\[ CP_2 = \frac{9900}{0.80} = 12375 \]

### Step 4: Calculate the total Cost Price (CP) of both cows
Now, we can find the total cost price of both cows:

\[ \text{Total CP} = CP_1 + CP_2 = 9000 + 12375 = 21375 \]

### Step 5: Calculate the total Selling Price (SP) of both cows
The total selling price of both cows is:

\[ \text{Total SP} = 9900 + 9900 = 19800 \]

### Step 6: Calculate the overall profit or loss
To find the overall profit or loss, we subtract the total cost price from the total selling price:

\[ \text{Overall Profit/Loss} = \text{Total SP} - \text{Total CP} = 19800 - 21375 = -1575 \]

Since the result is negative, it indicates a loss.

### Step 7: Calculate the percentage of loss
To find the percentage of loss, we use the formula:

\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Total CP}} \right) \times 100 \]

Substituting the values:

\[ \text{Loss Percentage} = \left( \frac{1575}{21375} \right) \times 100 \approx 7.375\% \]

### Final Result
The overall loss is Rs. 1575, which is approximately 7.375%.

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