Rahim bought a T.V. with 20% discount on list price. Had he bought it with 25% discount the would have saved Rs. 500. At what price did he buy the T.V ?

Options

A. Rs. 16,000
B. Rs. 12,000
C. Rs. 10,000
D. Rs. 8,000

Answer

To solve the problem step by step, we will first define the variables and then use the information provided in the question to find the price at which Rahim bought the TV.

### Step 1: Define the List Price
Let the list price of the TV be \( P \).

### Step 2: Calculate the Price with 20% Discount
When Rahim buys the TV with a 20% discount, he pays:
\[ \text{Price paid} = P - 0.20P = 0.80P \]

### Step 3: Calculate the Price with 25% Discount
If he had bought the TV with a 25% discount, he would pay:
\[ \text{Price paid with 25% discount} = P - 0.25P = 0.75P \]

### Step 4: Set Up the Equation Based on Savings
According to the problem, the difference in price between the two discounts is Rs. 500. Therefore, we can set up the equation:
\[ 0.80P - 0.75P = 500 \]

### Step 5: Simplify the Equation
Simplifying the left side gives:
\[ 0.05P = 500 \]

### Step 6: Solve for the List Price \( P \)
To find \( P \), divide both sides by 0.05:
\[ P = \frac{500}{0.05} = 10000 \]

### Step 7: Calculate the Price Rahim Paid
Now that we have the list price, we can find the price Rahim actually paid for the TV:
\[ \text{Price paid} = 0.80P = 0.80 \times 10000 = 8000 \]

### Final Answer
Rahim bought the TV for Rs. 8000.

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