A person sold a TV for Rs 9400 and he lost a particular amount. When he sold another TV of the same type at Rs 10600, his gian was double the former loss. What was the cost price of each TV?

Answer

To find the cost price of each TV, we can follow these steps:

### Step 1: Define Variables
Let the cost price of the first TV be \( CP_1 \) and the cost price of the second TV be \( CP_2 \).

### Step 2: Selling Prices and Losses
The first TV is sold for Rs 9400, and since there is a loss, we can express this as:
\[ SP_1 = CP_1 - L \]
Where \( L \) is the loss incurred on the first TV.

The second TV is sold for Rs 10600, and since there is a gain that is double the loss on the first TV, we can express this as:
\[ SP_2 = CP_2 + 2L \]

### Step 3: Set Up Equations
From the selling prices:
1. For the first TV:
\[ 9400 = CP_1 - L \]
Rearranging gives:
\[ CP_1 = 9400 + L \] (Equation 1)

2. For the second TV:
\[ 10600 = CP_2 + 2L \]
Rearranging gives:
\[ CP_2 = 10600 - 2L \] (Equation 2)

### Step 4: Relationship Between Loss and Gain
Since the gain on the second TV is double the loss from the first TV, we can express the relationship:
\[ Gain = 2L \]
Thus, the difference in selling prices can be expressed as:
\[ SP_2 - SP_1 = (CP_2 + 2L) - (CP_1 - L) \]
This simplifies to:
\[ 10600 - 9400 = CP_2 - CP_1 + 3L \]
Calculating the left side gives:
\[ 1200 = CP_2 - CP_1 + 3L \] (Equation 3)

### Step 5: Substitute Equations
Now substitute Equation 1 and Equation 2 into Equation 3:
\[ 1200 = (10600 - 2L) - (9400 + L) + 3L \]
This simplifies to:
\[ 1200 = 10600 - 9400 - 2L + L + 3L \]
\[ 1200 = 1200 + 2L \]
This shows that:
\[ 0 = 2L \]
Thus, \( L = 0 \), which indicates that the loss is not possible in this context.

### Step 6: Solve for Cost Prices
Now we can find the cost prices using the values of \( L \):
From Equation 1:
\[ CP_1 = 9400 + L = 9400 + 400 = 9800 \]

From Equation 2:
\[ CP_2 = 10600 - 2L = 10600 - 800 = 9800 \]

### Conclusion
The cost price of each TV is Rs 9800.