To solve this problem, let's start by determining the cost price of the television, and then use it to find the gain or loss percent when the television is sold for Rs. 3445.
### Step 1: Determine the Cost Price of the Television
- We are given:
- Selling price when sold at a loss = Rs. 3120
- Loss percentage = 4%
- We can use the formula for loss percent:
[tex]\[
\text{Loss} = \left( \frac{\text{Loss percent}}{100} \right) \times \text{Cost Price}
\][/tex]
Since selling price = cost price - loss,
[tex]\[
3120 = \text{Cost Price} \times \left(1 - \frac{4}{100}\right)
\][/tex]
- We now solve for the cost price (CP):
[tex]\[
3120 = \text{Cost Price} \times 0.96
\][/tex]
[tex]\[
\text{Cost Price} = \frac{3120}{0.96} = 3250
\][/tex]
So the cost price of the television is Rs. 3250.
### Step 2: Calculate the Gain or Loss Percentage when Sold for Rs. 3445
- We are given a new selling price = Rs. 3445
- We use the formula for gain/loss percent:
[tex]\[
\text{Gain or Loss} = \text{Selling Price} - \text{Cost Price}
\][/tex]
[tex]\[
\text{Gain or Loss Percent} = \left( \frac{\text{Gain or Loss}}{\text{Cost Price}} \right) \times 100
\][/tex]
- First, calculate the gain:
[tex]\[
\text{Gain} = 3445 - 3250 = 195
\][/tex]
- Now, calculate the gain percent:
[tex]\[
\text{Gain Percent} = \left( \frac{195}{3250} \right) \times 100 \approx 6
\][/tex]
Thus, when the television is sold for Rs. 3445, the gain percentage is 6%.
