A person sells his T.V. at 25% profit of the cost price. If he sells his T.V. at 25% profit of the selling price then his profit is increased by `(5%` of C.P. + 8 Rs.). Find the cost price of T.V.

Options

A. 640
B. 800
C. 632
D. 750

Answer

To solve the problem, we need to find the cost price (C.P.) of the T.V. Let's denote the cost price of the T.V. as \( C \).

### Step-by-Step Solution:

1. **Calculate the Selling Price with 25% Profit on C.P.**:
- The selling price (S.P.) when sold at 25% profit on the cost price is given by:
\[ S.P. = C + 0.25C = 1.25C \]

2. **Calculate the New Selling Price with 25% Profit on S.P.**:
- If the T.V. is sold at 25% profit on the selling price, we need to find the new selling price. The new selling price (let's denote it as \( S.P' \)) can be calculated as:
\[ S.P' = S.P. + 0.25 \times S.P. = 1.25S.P. = 1.25 \times 1.25C = 1.5625C \]

3. **Calculate the Profit from the New Selling Price**:
- The profit when sold at the new selling price is:
\[ \text{Profit} = S.P' - C = 1.5625C - C = 0.5625C \]

4. **Calculate the Increase in Profit**:
- According to the problem, the increase in profit is given as \( 5\% \) of C.P. plus \( 8 \) Rs. This can be expressed as:
\[ \text{Increase in Profit} = 0.05C + 8 \]

5. **Set Up the Equation**:
- The increase in profit from the original profit (which was \( 0.25C \)) to the new profit (which is \( 0.5625C \)) can be expressed as:
\[ 0.5625C - 0.25C = 0.05C + 8 \]
- Simplifying the left side:
\[ 0.3125C = 0.05C + 8 \]

6. **Solve for C**:
- Rearranging the equation:
\[ 0.3125C - 0.05C = 8 \]
\[ 0.2625C = 8 \]
\[ C = \frac{8}{0.2625} \approx 30.4 \]

### Final Answer:
The cost price of the T.V. is approximately \( 30.4 \) Rs.