Kamal sold two scooters for Rs. 19800 each, gaining 10% on the one and losing 10% on the other. Find his gain or loss per cent on the whole transaction.

Answer

To solve the problem step by step, we will calculate the cost price of each scooter based on the selling price and the gain/loss percentages, then find the total cost price and selling price to determine the overall gain or loss percentage.

### Step 1: Determine the Selling Price of Each Scooter
The selling price (SP) of each scooter is given as Rs. 19,800.

### Step 2: Calculate the Cost Price of the First Scooter
Kamal gains 10% on the first scooter. We can use the formula for selling price in terms of cost price and gain percentage:

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

Where Gain can be expressed as:

\[ \text{Gain} = \frac{\text{Gain Percentage}}{100} \times CP \]

Let the cost price of the first scooter be \( X \).

Then,

\[ 19,800 = X + \frac{10}{100} \times X \]

This simplifies to:

\[ 19,800 = X + 0.1X = 1.1X \]

Now, solving for \( X \):

\[ X = \frac{19,800}{1.1} = 18,000 \]

So, the cost price of the first scooter is Rs. 18,000.

### Step 3: Calculate the Cost Price of the Second Scooter
Kamal loses 10% on the second scooter. Using a similar approach:

Let the cost price of the second scooter be \( Y \).

The loss can be expressed as:

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

Where Loss is:

\[ \text{Loss} = \frac{\text{Loss Percentage}}{100} \times CP \]

Thus,

\[ 19,800 = Y - \frac{10}{100} \times Y \]

This simplifies to:

\[ 19,800 = Y - 0.1Y = 0.9Y \]

Now, solving for \( Y \):

\[ Y = \frac{19,800}{0.9} = 22,000 \]

So, the cost price of the second scooter is Rs. 22,000.

### Step 4: Calculate the Total Cost Price and Total Selling Price
Now, we can find the total cost price and total selling price for both scooters:

- Total Cost Price (CP) = Cost Price of First Scooter + Cost Price of Second Scooter
\[ CP = 18,000 + 22,000 = 40,000 \]

- Total Selling Price (SP) = Selling Price of First Scooter + Selling Price of Second Scooter
\[ SP = 19,800 + 19,800 = 39,600 \]

### Step 5: Determine Overall Gain or Loss
To find the overall gain or loss, we subtract the total selling price from the total cost price:

\[ \text{Loss} = CP - SP = 40,000 - 39,600 = 400 \]

### Step 6: Calculate the Loss Percentage
Finally, we can calculate the loss percentage using the formula:

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

Substituting the values:

\[ \text{Loss Percentage} = \left(\frac{400}{40,000}\right) \times 100 = 1\% \]

### Conclusion
Kamal incurred a loss of 1% on the whole transaction.

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