Hema bought two pairs of jeans for Rs. 1450 each. She sold one of them at a gain of 8% and the other at a loss of 4%.Find her gain or loss per cent in the whole transaction.

Answer

Let's solve the problem step by step.

### Step 1: Determine the Cost Price (CP) of each pair of jeans.
Hema bought two pairs of jeans for Rs. 1450 each.

**Cost Price of each pair of jeans = Rs. 1450**

### Step 2: Calculate the Selling Price (SP) of the first pair of jeans.
The first pair of jeans is sold at a gain of 8%.

To find the Selling Price (SP) when there is a gain, we use the formula:
\[ SP = CP \times \left(1 + \frac{\text{Gain\%}}{100}\right) \]

Substituting the values:
\[ SP_1 = 1450 \times \left(1 + \frac{8}{100}\right) = 1450 \times \left(1 + 0.08\right) = 1450 \times 1.08 \]
Calculating this gives:
\[ SP_1 = 1566 \]

### Step 3: Calculate the Selling Price (SP) of the second pair of jeans.
The second pair of jeans is sold at a loss of 4%.

To find the Selling Price (SP) when there is a loss, we use the formula:
\[ SP = CP \times \left(1 - \frac{\text{Loss\%}}{100}\right) \]

Substituting the values:
\[ SP_2 = 1450 \times \left(1 - \frac{4}{100}\right) = 1450 \times \left(1 - 0.04\right) = 1450 \times 0.96 \]
Calculating this gives:
\[ SP_2 = 1392 \]

### Step 4: Calculate the Total Cost Price (CP) and Total Selling Price (SP).
**Total Cost Price (CP)**:
\[ \text{Total CP} = CP_1 + CP_2 = 1450 + 1450 = 2900 \]

**Total Selling Price (SP)**:
\[ \text{Total SP} = SP_1 + SP_2 = 1566 + 1392 = 2958 \]

### Step 5: Calculate the Gain or Loss.
To find the gain or loss, we subtract the Total CP from the Total SP:
\[ \text{Gain} = \text{Total SP} - \text{Total CP} = 2958 - 2900 = 58 \]

### Step 6: Calculate the Gain Percentage.
To find the gain percentage, we use the formula:
\[ \text{Gain\%} = \left(\frac{\text{Gain}}{\text{Total CP}}\right) \times 100 \]

Substituting the values:
\[ \text{Gain\%} = \left(\frac{58}{2900}\right) \times 100 \]
Calculating this gives:
\[ \text{Gain\%} = 2 \]

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

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