An article is sold for Rs. 6500 so as to earn a profit of `4%` A second article whose cost price is Rs. 3750,is sold at a loss of `4%` .What is the overall gain or loss percent in the whole transaction ?

Options

A. Gain `4%`
B. `Loss `1%`
C. Loss `4%`
D. Gain `1%`

Answer

To solve the problem step by step, we will break it down into manageable parts.

### Step 1: Calculate the Cost Price (CP) of the First Article
The selling price (SP) of the first article is Rs. 6500, and it is sold at a profit of 4%.

Using the formula:
\[ SP = CP + \text{Profit} \]
Where:
\[ \text{Profit} = \frac{\text{Profit Percent}}{100} \times CP \]
We can express SP in terms of CP:
\[ SP = CP + \frac{4}{100} \times CP = CP \left(1 + \frac{4}{100}\right) = CP \times \frac{104}{100} \]

Setting this equal to the selling price:
\[ 6500 = CP \times \frac{104}{100} \]

Now, we can solve for CP:
\[ CP = \frac{6500 \times 100}{104} = \frac{650000}{104} \approx 6250 \]

### Step 2: Calculate the Selling Price (SP) of the Second Article
The cost price (CP) of the second article is Rs. 3750, and it is sold at a loss of 4%.

Using the formula:
\[ SP = CP - \text{Loss} \]
Where:
\[ \text{Loss} = \frac{\text{Loss Percent}}{100} \times CP \]
We can express SP in terms of CP:
\[ SP = CP - \frac{4}{100} \times CP = CP \left(1 - \frac{4}{100}\right) = CP \times \frac{96}{100} \]

Now substituting the CP:
\[ SP = 3750 \times \frac{96}{100} = 3750 \times 0.96 = 3600 \]

### Step 3: Calculate Total Cost Price (Total CP) and Total Selling Price (Total SP)
Now we can find the total cost price and total selling price:
\[ \text{Total CP} = CP_{\text{first}} + CP_{\text{second}} = 6250 + 3750 = 10000 \]
\[ \text{Total SP} = SP_{\text{first}} + SP_{\text{second}} = 6500 + 3600 = 10100 \]

### Step 4: Calculate Overall Gain or Loss
To find the overall gain or loss, we subtract the total CP from the total SP:
\[ \text{Overall Gain} = \text{Total SP} - \text{Total CP} = 10100 - 10000 = 100 \]

### Step 5: Calculate Overall Gain Percent
To find the overall gain percent, we use the formula:
\[ \text{Gain Percent} = \left(\frac{\text{Overall Gain}}{\text{Total CP}}\right) \times 100 \]
Substituting the values:
\[ \text{Gain Percent} = \left(\frac{100}{10000}\right) \times 100 = 1\% \]

### Final Answer
The overall gain percent in the whole transaction is **1%**.

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