The cost of 2 T.V sets and a radio is Rs. 7000, While 2 radios and one T.V set together cost Rs. 4250. The cost of a T.V. set is

Options

A. Rs. 3000
B. Rs. 3160
C. Rs. 3240
D. None of these

Answer

To find the cost of a T.V. set, we can set up the problem using algebra. Let's denote the cost of one T.V. set as \( T \) and the cost of one radio as \( R \).

### Step 1: Set up the equations
From the problem, we have the following two equations based on the information provided:

1. \( 2T + R = 7000 \) (Equation 1)
2. \( T + 2R = 4250 \) (Equation 2)

### Step 2: Solve for one variable
We can solve one of the equations for one variable. Let's solve Equation 1 for \( R \):

\[ R = 7000 - 2T \]

### Step 3: Substitute into the second equation
Now, we substitute \( R \) from Equation 1 into Equation 2:

\[ T + 2(7000 - 2T) = 4250 \]

### Step 4: Simplify the equation
Expanding the equation gives us:

\[ T + 14000 - 4T = 4250 \]

Combining like terms:

\[ -3T + 14000 = 4250 \]

### Step 5: Isolate \( T \)
Now, we isolate \( T \):

\[ -3T = 4250 - 14000 \]
\[ -3T = -9750 \]
\[ T = \frac{9750}{3} \]
\[ T = 3250 \]

### Step 6: Conclusion
Thus, the cost of one T.V. set is Rs. 3250.