Two articles each is sold at Rs. 4880. On one article the seller gains 18% and on the other he loses 16%. What is his overall gain or loss percent to nearest one decimal place ?

Options

A. `2.1% "loss "`
B. `1.9% "loss "`
C. `2.4% "gain "`
D. `1.9% "gain" `

Answer

To solve the problem step by step, we will calculate the cost price (CP) of each article based on the selling price (SP) and the respective gain or loss percentages. Then, we will find the overall gain or loss percentage.

### Step 1: Identify the Selling Price (SP)
Given:
- Selling Price (SP) of each article = Rs. 4880

### Step 2: Calculate the Cost Price (CP) of the first article (with 18% gain)
The formula to calculate CP when the gain percentage is known:
\[ CP = \frac{SP \times 100}{100 + \text{Gain \%}} \]

For the first article:
- Gain % = 18%
- Therefore,
\[ CP_1 = \frac{4880 \times 100}{100 + 18} = \frac{4880 \times 100}{118} \]
Calculating this gives:
\[ CP_1 \approx \frac{488000}{118} \approx 4135.59 \]

### Step 3: Calculate the Cost Price (CP) of the second article (with 16% loss)
The formula to calculate CP when the loss percentage is known:
\[ CP = \frac{SP \times 100}{100 - \text{Loss \%}} \]

For the second article:
- Loss % = 16%
- Therefore,
\[ CP_2 = \frac{4880 \times 100}{100 - 16} = \frac{4880 \times 100}{84} \]
Calculating this gives:
\[ CP_2 \approx \frac{488000}{84} \approx 5809.52 \]

### Step 4: Calculate the Total Cost Price (CP)
Now, we will sum the cost prices of both articles:
\[ \text{Total CP} = CP_1 + CP_2 = 4135.59 + 5809.52 \approx 9945.11 \]

### Step 5: Calculate the Total Selling Price (SP)
Since both articles are sold for the same price:
\[ \text{Total SP} = SP_1 + SP_2 = 4880 + 4880 = 9760 \]

### Step 6: Determine Overall Gain or Loss
To find out if there is a gain or loss:
\[ \text{Gain/Loss} = \text{Total SP} - \text{Total CP} \]
Calculating this gives:
\[ \text{Gain/Loss} = 9760 - 9945.11 \approx -185.11 \]
This indicates a loss of Rs. 185.11.

### Step 7: Calculate the Loss Percentage
The formula for loss percentage is:
\[ \text{Loss \%} = \left( \frac{\text{Loss}}{\text{Total CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Loss \%} = \left( \frac{185.11}{9945.11} \right) \times 100 \approx 1.86\% \]

### Step 8: Round to the Nearest One Decimal Place
Rounding 1.86% gives us:
\[ \text{Loss \%} \approx 1.9\% \]

### Final Answer
The overall loss percentage is **1.9%**.