A TV set is being sold for Rs. X in Delhi. A dealer went to chandigarh and bought the TV at `20%` discount (from the price of the Delhi ) . He spent Rs. 600 on transport . Thus he sold the set in Delhi for Rs.X making `((100)/(7))%` profit What is the value of X ?
a) Rs. 7200
b) Rs. 8000
c) Rs. 8800
d) Rs. 9600

Options

A. Rs. 7200
B. Rs. 8000
C. Rs. 8800
D. Rs. 9600

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Discount
The dealer bought the TV at a 20% discount from the price in Delhi (Rs. X).
- The price after a 20% discount is:
\[ \text{Price after discount} = X - 0.20X = 0.80X = \frac{4}{5}X \]

### Step 2: Add Transportation Cost
The dealer spent Rs. 600 on transportation. Therefore, the total cost incurred by the dealer is:
\[ \text{Total cost} = \text{Price after discount} + \text{Transportation cost} = \frac{4}{5}X + 600 \]

### Step 3: Calculate Selling Price with Profit
The dealer sold the TV for Rs. X, making a profit of \(\frac{100}{7}\%\).
- To find the selling price in terms of cost price and profit percentage, we can use the formula:
\[ \text{Selling Price} = \text{Cost Price} + \text{Profit} \]
- The profit can be calculated as:
\[ \text{Profit} = \frac{100}{7}\% \text{ of Cost Price} = \frac{100}{7} \times \text{Cost Price} \]
- The selling price can also be expressed as:
\[ X = \text{Cost Price} + \frac{100}{7} \times \text{Cost Price} = \left(1 + \frac{100}{7}\right) \times \text{Cost Price} = \frac{7 + 100}{7} \times \text{Cost Price} = \frac{107}{7} \times \text{Cost Price} \]

### Step 4: Set Up the Equation
Now we can set up the equation:
\[ X = \frac{107}{7} \left(\frac{4}{5}X + 600\right) \]

### Step 5: Clear the Fraction
Multiply both sides by 7 to eliminate the fraction:
\[ 7X = 107 \left(\frac{4}{5}X + 600\right) \]

### Step 6: Distribute and Simplify
Distributing the 107:
\[ 7X = \frac{428}{5}X + 64200 \]

### Step 7: Get a Common Denominator
Multiply the entire equation by 5 to eliminate the fraction:
\[ 35X = 428X + 321000 \]

### Step 8: Rearranging the Equation
Rearranging gives:
\[ 35X - 428X = 321000 \]
\[ -393X = 321000 \]
\[ X = \frac{321000}{393} \]

### Step 9: Calculate X
Calculating the value:
\[ X = 8000 \]

### Conclusion
Thus, the value of X is Rs. 8000.