A person sells T.V. at 20% profit. If he gets profit equal to 20% S.P. then he would gain (3% of C.P. + 83 Rs) more. Find C.P. of T.V.?

Answer

To solve the problem step by step, we need to define some variables and use the information given in the question.

### Step 1: Define Variables
Let the Cost Price (C.P.) of the T.V. be \( x \).

### Step 2: Calculate Selling Price (S.P.) with 20% Profit
The Selling Price (S.P.) when sold at a 20% profit can be calculated as:
\[ S.P. = C.P. + 20\% \text{ of } C.P. = x + 0.2x = 1.2x \]

### Step 3: Calculate Profit Equal to 20% of S.P.
The profit equal to 20% of S.P. is:
\[ 20\% \text{ of } S.P. = 0.2 \times S.P. = 0.2 \times 1.2x = 0.24x \]

### Step 4: Set Up the Equation
According to the problem, if he gets a profit equal to 20% of S.P., he would gain \( 3\% \text{ of } C.P. + 83 \text{ Rs} \) more. Therefore, we can set up the equation:
\[ 0.24x = 0.03x + 83 \]

### Step 5: Solve the Equation
Now, we will solve for \( x \):
\[ 0.24x - 0.03x = 83 \]
\[ 0.21x = 83 \]
\[ x = \frac{83}{0.21} \]
\[ x = 395.24 \text{ Rs (approximately)} \]

### Conclusion
The Cost Price (C.P.) of the T.V. is approximately \( 395.24 \text{ Rs} \).