A man sells a television set at a profit of 10%. If he had bought it for 10% less and sold it for Rs. 360 less, he would have gained 20%. Find the cost price of the television set.

Options

A. Rs. 18000
B. 18500
C. Rs. 17000
D. Rs. 19000

Answer

To solve the problem, we will break it down step by step.

### Step 1: Define the Cost Price (CP)
Let the cost price of the television set be \( CP \).

### Step 2: Selling Price (SP) with 10% Profit
If the man sells the television set at a profit of 10%, then the selling price (SP) can be calculated as:
\[ SP = CP + 10\% \text{ of } CP = CP + 0.1 \times CP = 1.1 \times CP \]

### Step 3: New Cost Price with 10% Less
If he had bought it for 10% less, the new cost price would be:
\[ New\ CP = CP - 10\% \text{ of } CP = CP - 0.1 \times CP = 0.9 \times CP \]

### Step 4: Selling Price with Rs. 360 Less
If he sells it for Rs. 360 less, the new selling price would be:
\[ New\ SP = SP - 360 = 1.1 \times CP - 360 \]

### Step 5: New Selling Price with 20% Profit
According to the problem, if he sells at this new price, he would gain 20% on the new cost price. Therefore, the new selling price can also be expressed as:
\[ New\ SP = New\ CP + 20\% \text{ of } New\ CP = 0.9 \times CP + 0.2 \times (0.9 \times CP) = 0.9 \times CP + 0.18 \times CP = 1.08 \times CP \]

### Step 6: Set Up the Equation
Now we can set the two expressions for the new selling price equal to each other:
\[ 1.1 \times CP - 360 = 1.08 \times CP \]

### Step 7: Solve for CP
Rearranging the equation gives:
\[ 1.1 \times CP - 1.08 \times CP = 360 \]
\[ 0.02 \times CP = 360 \]
\[ CP = \frac{360}{0.02} = 18000 \]

### Conclusion
Thus, the cost price of the television set is:
\[ \boxed{18000} \]