To solve the problem step by step, we will denote the cost price of the radio as \( X \) and the cost price of the TV set as \( Y \).
### Step 1: Set up the equations based on the selling prices and profits.
1. **First Selling Price**: The man sold the radio and TV set together for Rs. 30,400 with a profit of 25% on the radio and 10% on the TV set.
- Selling Price of Radio = \( 1.25X \)
- Selling Price of TV = \( 1.10Y \)
- Therefore, we can write the first equation:
\[
1.25X + 1.10Y = 30,400 \quad \text{(Equation 1)}
\]
2. **Second Selling Price**: If he sold them together for Rs. 30,700, he would have made a 10% profit on the radio and a 25% profit on the TV set.
- Selling Price of Radio = \( 1.10X \)
- Selling Price of TV = \( 1.25Y \)
- Thus, we can write the second equation:
\[
1.10X + 1.25Y = 30,700 \quad \text{(Equation 2)}
\]
### Step 2: Solve the equations simultaneously.
We have the following two equations:
1. \( 1.25X + 1.10Y = 30,400 \) (Equation 1)
2. \( 1.10X + 1.25Y = 30,700 \) (Equation 2)
We can multiply Equation 1 by 1.10 and Equation 2 by 1.25 to eliminate \( Y \).
- **Multiply Equation 1 by 1.10**:
\[
1.375X + 1.21Y = 33,440 \quad \text{(Equation 3)}
\]
- **Multiply Equation 2 by 1.25**:
\[
1.375X + 1.5625Y = 38,375 \quad \text{(Equation 4)}
\]
### Step 3: Subtract Equation 3 from Equation 4.
Now we subtract Equation 3 from Equation 4:
\[
(1.375X + 1.5625Y) - (1.375X + 1.21Y) = 38,375 - 33,440
\]
This simplifies to:
\[
0.3525Y = 4,935
\]
### Step 4: Solve for \( Y \).
Now, divide both sides by 0.3525:
\[
Y = \frac{4,935}{0.3525} = 14,000
\]
### Step 5: Substitute \( Y \) back to find \( X \).
Now that we have \( Y \), we can substitute it back into either Equation 1 or Equation 2 to find \( X \). We will use Equation 1:
\[
1.25X + 1.10(14,000) = 30,400
\]
This simplifies to:
\[
1.25X + 15,400 = 30,400
\]
Subtracting 15,400 from both sides:
\[
1.25X = 15,000
\]
Now, divide by 1.25:
\[
X = \frac{15,000}{1.25} = 12,000
\]
### Final Answer:
The cost price of the radio is Rs. 12,000.
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