If two mixers and one T.V. cost Rs. 7000, while two T.V.s and one mixer cost Rs. 9800. The value of one T.V is-

Options

A. Rs. 2800
B. Rs. 2100
C. Rs. 4200
D. Rs. 8400

Answer

To solve the problem, we need to set up equations based on the information given. Let's denote the cost of one mixer as \( x \) and the cost of one TV as \( y \).

### Step 1: Set up the equations
From the problem, we have two pieces of information:
1. Two mixers and one TV cost Rs. 7000:
\[ 2x + y = 7000 \quad \text{(Equation 1)} \]
2. Two TVs and one mixer cost Rs. 9800:
\[ 2y + x = 9800 \quad \text{(Equation 2)} \]

### Step 2: Solve Equation 1 for \( y \)
From Equation 1, we can express \( y \) in terms of \( x \):
\[ y = 7000 - 2x \quad \text{(Substituting into Equation 1)} \]

### Step 3: Substitute \( y \) in Equation 2
Now, substitute \( y \) from Equation 1 into Equation 2:
\[ 2(7000 - 2x) + x = 9800 \]
Expanding this gives:
\[ 14000 - 4x + x = 9800 \]
Combining like terms:
\[ 14000 - 3x = 9800 \]

### Step 4: Isolate \( x \)
Now, isolate \( x \):
\[ -3x = 9800 - 14000 \]
\[ -3x = -4200 \]
Dividing both sides by -3:
\[ x = 1400 \]

### Step 5: Substitute \( x \) back to find \( y \)
Now that we have \( x \), we can find \( y \) using Equation 1:
\[ y = 7000 - 2(1400) \]
\[ y = 7000 - 2800 \]
\[ y = 4200 \]

### Conclusion
The value of one TV is Rs. 4200.

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