A shopkeeper sells TV at Rs 40,250. He sells 6 TV sets in a day and earns a profit of Rs 31,500. Find the cost price and the gain per cent of one TV.

Answer

To solve the problem step by step, we will follow the given information and apply the relevant formulas.

### Step 1: Write down the given information
- Selling Price (SP) of 1 TV = Rs 40,250
- Profit on 6 TVs = Rs 31,500

### Step 2: Calculate the profit on 1 TV
To find the profit on one TV, we divide the total profit by the number of TVs sold.

\[ \text{Profit on 1 TV} = \frac{\text{Profit on 6 TVs}}{6} = \frac{31,500}{6} \]

Calculating this gives:

\[ \text{Profit on 1 TV} = 5,250 \text{ Rs} \]

### Step 3: Calculate the Cost Price (CP) of 1 TV
We know that:

\[ \text{Selling Price} - \text{Cost Price} = \text{Profit} \]

Rearranging this formula gives us:

\[ \text{Cost Price} = \text{Selling Price} - \text{Profit} \]

Substituting the known values:

\[ \text{Cost Price} = 40,250 - 5,250 \]

Calculating this gives:

\[ \text{Cost Price} = 35,000 \text{ Rs} \]

### Step 4: Calculate the Gain Percentage
The gain percentage can be calculated using the formula:

\[ \text{Gain Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]

Substituting the known values:

\[ \text{Gain Percentage} = \left( \frac{5,250}{35,000} \right) \times 100 \]

Calculating this gives:

\[ \text{Gain Percentage} = \left( \frac{5,250}{35,000} \right) \times 100 = 15\% \]

### Final Answers
- Cost Price of 1 TV = Rs 35,000
- Gain Percentage of 1 TV = 15%

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