Mehta Radios sell one radio for Rs.840 at a gain of `20%` and another for Rs.960 at a loss of `4%`. What total gain or loss percentage?

Options

A. 5
B. 6
C. `6 (12)/17%`
D. `5 (15)/17%`

Answer

To solve the problem, we need to find the total gain or loss percentage from selling two radios. Let's break it down step by step.

### Step 1: Calculate the Cost Price of the First Radio
The first radio is sold for Rs. 840 at a gain of 20%.

Using the formula for selling price (SP) with gain:
\[ SP = CP + \text{Gain} \]
Where Gain = \( \frac{\text{Gain \%}}{100} \times CP \)

Given that Gain = 20%, we can express the selling price as:
\[ SP = CP + \frac{20}{100} \times CP = CP \times \left(1 + \frac{20}{100}\right) = CP \times 1.2 \]

Thus, we can rearrange to find the cost price (CP):
\[ CP = \frac{SP}{1.2} \]
Substituting the selling price:
\[ CP = \frac{840}{1.2} = 700 \]

### Step 2: Calculate the Cost Price of the Second Radio
The second radio is sold for Rs. 960 at a loss of 4%.

Using the formula for selling price (SP) with loss:
\[ SP = CP - \text{Loss} \]
Where Loss = \( \frac{\text{Loss \%}}{100} \times CP \)

Given that Loss = 4%, we can express the selling price as:
\[ SP = CP - \frac{4}{100} \times CP = CP \times \left(1 - \frac{4}{100}\right) = CP \times 0.96 \]

Thus, we can rearrange to find the cost price (CP):
\[ CP = \frac{SP}{0.96} \]
Substituting the selling price:
\[ CP = \frac{960}{0.96} = 1000 \]

### Step 3: Calculate Total Selling Price and Total Cost Price
Now, we can find the total selling price (SP_total) and total cost price (CP_total):

Total Selling Price:
\[ SP_{\text{total}} = 840 + 960 = 1800 \]

Total Cost Price:
\[ CP_{\text{total}} = 700 + 1000 = 1700 \]

### Step 4: Calculate Total Gain
Now, we can calculate the total gain:
\[ \text{Total Gain} = SP_{\text{total}} - CP_{\text{total}} = 1800 - 1700 = 100 \]

### Step 5: Calculate Gain Percentage
Finally, we can find the gain percentage:
\[ \text{Gain Percentage} = \left(\frac{\text{Total Gain}}{CP_{\text{total}}}\right) \times 100 = \left(\frac{100}{1700}\right) \times 100 \approx 5.88\% \]

### Final Answer
The total gain percentage is approximately **5.88%**.

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