A shopkeeper sold a TV a 16% discount on print rate. If the customer is paid Rs. 9828 for the TV and the printed price is 20% more than its cost price, what is the cost price of TV ?

Options

A. Rs. 9875
B. Rs. 9450
C. Rs. 9750
D. Rs. 9850

Answer

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

### Step 1: Define Variables
Let the cost price (CP) of the TV be \( x \).

### Step 2: Calculate the Marked Price (MP)
The marked price is 20% more than the cost price. Therefore, we can express the marked price as:
\[ MP = CP + 20\% \text{ of } CP = x + 0.2x = 1.2x \]

### Step 3: Calculate the Selling Price (SP)
The shopkeeper sold the TV at a 16% discount on the marked price. The selling price can be calculated as:
\[ SP = MP - 16\% \text{ of } MP = MP - 0.16 \times MP = MP \times (1 - 0.16) = MP \times 0.84 \]
Substituting the expression for MP:
\[ SP = 0.84 \times (1.2x) = 1.008x \]

### Step 4: Set Up the Equation
According to the problem, the selling price is Rs. 9828. Therefore, we can set up the equation:
\[ 1.008x = 9828 \]

### Step 5: Solve for x
To find the cost price, we can solve for \( x \):
\[ x = \frac{9828}{1.008} \]
Calculating this gives:
\[ x = 9748.81 \approx 9750 \text{ (rounding to the nearest whole number)} \]

### Step 6: Calculate the Cost Price
Since we defined \( x \) as the cost price, we conclude that:
\[ CP = 9750 \]

### Final Answer
The cost price of the TV is Rs. 9750.

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