Manohar purchased two handbags for Rs.1500 each. He sold these bags, gaining 8% on one and losing 4% on the other. Find his gain or loss percent in the whole transaction.

Answer

To solve the problem step by step, we will calculate the selling prices of both handbags, the total cost price, the total selling price, and finally the overall gain or loss percentage.

### Step 1: Calculate the Selling Price of the First Handbag
Manohar purchased the first handbag for Rs. 1500 and sold it at an 8% gain.

**Formula for Selling Price (SP) with Gain:**
\[ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Gain \%}}{100}\right) \]

**Calculation:**
\[ \text{SP of First Handbag} = 1500 \times \left(1 + \frac{8}{100}\right) = 1500 \times \left(1 + 0.08\right) = 1500 \times 1.08 = 1620 \]

### Step 2: Calculate the Selling Price of the Second Handbag
Manohar purchased the second handbag for Rs. 1500 and sold it at a 4% loss.

**Formula for Selling Price (SP) with Loss:**
\[ \text{SP} = \text{CP} \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]

**Calculation:**
\[ \text{SP of Second Handbag} = 1500 \times \left(1 - \frac{4}{100}\right) = 1500 \times \left(1 - 0.04\right) = 1500 \times 0.96 = 1440 \]

### Step 3: Calculate the Total Cost Price
The total cost price (CP) of both handbags is:
\[ \text{Total CP} = \text{CP of First Handbag} + \text{CP of Second Handbag} = 1500 + 1500 = 3000 \]

### Step 4: Calculate the Total Selling Price
The total selling price (SP) of both handbags is:
\[ \text{Total SP} = \text{SP of First Handbag} + \text{SP of Second Handbag} = 1620 + 1440 = 3060 \]

### Step 5: Calculate the Overall Gain
To find the overall gain:
\[ \text{Gain} = \text{Total SP} - \text{Total CP} = 3060 - 3000 = 60 \]

### Step 6: Calculate the Gain Percentage
To find the gain percentage:
\[ \text{Gain \%} = \left(\frac{\text{Gain}}{\text{Total CP}}\right) \times 100 = \left(\frac{60}{3000}\right) \times 100 = 2\% \]

### Final Answer
Manohar's overall gain percentage in the whole transaction is **2%**.

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