Luxmi sold two sarees for Rs.1980 each. On one, she lost 10%. While on the other she gained 10%. Find gain or loss percent in the whole transaction.

Answer

To solve the problem step by step, we need to calculate the cost price of each saree and then determine the overall gain or loss percentage from the entire transaction.

### Step 1: Calculate the Selling Price of Each Saree
Luxmi sold each saree for Rs. 1980.

**Selling Price (SP) of each saree = Rs. 1980**

### Step 2: Calculate the Cost Price of the Saree Sold at a Loss
For the saree sold at a loss of 10%, we can use the formula:

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

Let the cost price of the saree sold at a loss be \( CP_1 \).

Since she lost 10%, we can express the selling price as:

\[ SP = CP_1 - \text{Loss} \]

Substituting the loss into the equation gives us:

\[ 1980 = CP_1 - \left(\frac{10}{100} \times CP_1\right) \]

This simplifies to:

\[ 1980 = CP_1 - 0.1 \times CP_1 \]
\[ 1980 = 0.9 \times CP_1 \]

Now, we can solve for \( CP_1 \):

\[ CP_1 = \frac{1980}{0.9} = 2200 \]

### Step 3: Calculate the Cost Price of the Saree Sold at a Gain
For the saree sold at a gain of 10%, we can use a similar approach.

Let the cost price of the saree sold at a gain be \( CP_2 \).

Since she gained 10%, we can express the selling price as:

\[ SP = CP_2 + \text{Gain} \]

Substituting the gain into the equation gives us:

\[ 1980 = CP_2 + \left(\frac{10}{100} \times CP_2\right) \]

This simplifies to:

\[ 1980 = CP_2 + 0.1 \times CP_2 \]
\[ 1980 = 1.1 \times CP_2 \]

Now, we can solve for \( CP_2 \):

\[ CP_2 = \frac{1980}{1.1} = 1800 \]

### Step 4: Calculate the Total Cost Price and Total Selling Price
Now we can calculate the total cost price (CP) and total selling price (SP) for both sarees.

\[ \text{Total CP} = CP_1 + CP_2 = 2200 + 1800 = 4000 \]
\[ \text{Total SP} = 1980 + 1980 = 3960 \]

### Step 5: Calculate the Overall Gain or Loss
Now we can find out if there was a gain or loss:

\[ \text{Total Loss} = \text{Total CP} - \text{Total SP} = 4000 - 3960 = 40 \]

### Step 6: Calculate the Loss Percentage
To find the loss percentage, we use the formula:

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

Substituting the values:

\[ \text{Loss Percentage} = \left(\frac{40}{4000}\right) \times 100 = 1\% \]

### Final Answer
Thus, Luxmi incurred a loss of **1%** in the whole transaction.

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