A person sells T.V. at 25% profit. If he gets profit equal to 25% S.P. then he would gain (5% of C.P. + 80 Rs) more. Find C.P. of T.V.?

Answer

To solve the problem, let's denote the Cost Price (C.P.) of the TV as \( x \).

1. **Calculate Selling Price (S.P.) with 25% Profit:**
The selling price when the person sells the TV at a 25% profit can be calculated as:
\[ S.P. = C.P. + 25\% \text{ of } C.P. = x + 0.25x = 1.25x \]

2. **Determine Profit Equal to 25% of S.P.:**
According to the problem, if the profit is equal to 25% of the selling price, we can express this as:
\[ \text{Profit} = 25\% \text{ of } S.P. = 0.25 \times S.P. = 0.25 \times 1.25x = 0.3125x \]

3. **Set Up the Equation with Additional Profit:**
The problem states that this profit (0.3125x) is equal to the original profit (which is 25% of C.P. = 0.25x) plus an additional \( 5\% \text{ of } C.P. + 80 \text{ Rs} \):
\[ 0.3125x = 0.25x + 0.05x + 80 \]

4. **Combine Like Terms:**
Combine the terms on the right side:
\[ 0.3125x = 0.25x + 0.05x + 80 \implies 0.3125x = 0.30x + 80 \]

5. **Isolate the Variable:**
Now, let's isolate \( x \):
\[ 0.3125x - 0.30x = 80 \implies 0.0125x = 80 \]

6. **Solve for C.P.:**
To find \( x \), divide both sides by 0.0125:
\[ x = \frac{80}{0.0125} = 6400 \]

Thus, the Cost Price (C.P.) of the TV is \( \text{Rs } 6400 \).