Ram bought a T.V. with 20% discount on the labelled price. Had he bought it with 30% discount he would have saved Rs 800. The value of the T.V. set that he bought is

Options

A. Rs 5,000
B. Rs 8,000
C. Rs 9,000
D. Rs 10,000

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Understand the discounts
Ram bought a T.V. with a 20% discount on the labeled price. If he had bought it with a 30% discount, he would have saved Rs. 800.

### Step 2: Define the labeled price
Let the labeled price of the T.V. be denoted as \( P \).

### Step 3: Calculate the price with 20% discount
The price Ram paid after a 20% discount can be calculated as:
\[ \text{Price paid} = P - 0.20P = 0.80P \]

### Step 4: Calculate the price with 30% discount
If Ram had bought the T.V. with a 30% discount, the price would be:
\[ \text{Price with 30% discount} = P - 0.30P = 0.70P \]

### Step 5: Set up the equation based on the savings
According to the problem, the difference between the two prices (the savings) is Rs. 800:
\[ 0.80P - 0.70P = 800 \]

### Step 6: Simplify the equation
Simplifying the left side gives:
\[ 0.10P = 800 \]

### Step 7: Solve for the labeled price \( P \)
To find \( P \), divide both sides by 0.10:
\[ P = \frac{800}{0.10} = 8000 \]

### Step 8: Calculate the price Ram paid
Now that we have the labeled price, we can find the price Ram actually paid:
\[ \text{Price paid} = 0.80P = 0.80 \times 8000 = 6400 \]

### Conclusion
The value of the T.V. set that Ram bought is Rs. 6400.

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