There are 4 different computers in the showrooms P,Q,R ,S the price of Q is 10% more then P the price of R is 12% more than Q the price of S is 10% less than R showroom offres 5% discount on all purchases before sales tax is calculated. The showroom collect 250rs for delivering any number of computer to the customer .The installation charge per computer of any model is Rs 750 charged by the showroom on the customer.
The showroom has earned `₹4,02,984` in total by selling computer of type p to customer the sales tax is 8% and the customer paid for the installation only and transported in his own vehicle what is original price of one P model computer if customer purchased 12 computers from showroom

Options

A. `₹29,120`
B. `₹32,000`
C. `₹15,390`
D. `₹29,090`

Answer

To find the original price of one P model computer, we can follow these steps:

### Step 1: Define the Variables
Let the original price of computer P be \( P \).

### Step 2: Calculate the Prices of Other Computers
- The price of Q is 10% more than P:
\[ Q = P + 0.1P = 1.1P \]
- The price of R is 12% more than Q:
\[ R = Q + 0.12Q = 1.12Q = 1.12 \times 1.1P = 1.232P \]
- The price of S is 10% less than R:
\[ S = R - 0.1R = 0.9R = 0.9 \times 1.232P = 1.1088P \]

### Step 3: Calculate the Discounted Price of P
The showroom offers a 5% discount on all purchases. Therefore, the discounted price of P is:
\[ \text{Discounted Price} = P - 0.05P = 0.95P \]

### Step 4: Calculate the Final Price Including Sales Tax
The sales tax is 8%, so the final price after including sales tax is:
\[ \text{Final Price} = \text{Discounted Price} + \text{Sales Tax} = 0.95P + 0.08 \times 0.95P = 0.95P \times 1.08 = 1.026P \]

### Step 5: Calculate the Total Selling Price for 12 Computers
If the customer purchased 12 computers, the total selling price is:
\[ \text{Total Selling Price} = 12 \times 1.026P = 12.312P \]

### Step 6: Include Installation Charges
The installation charge per computer is Rs. 750. For 12 computers, the total installation charge is:
\[ \text{Total Installation Charge} = 12 \times 750 = 9000 \]

### Step 7: Total Amount Earned by the Showroom
The showroom earned a total of Rs. 402984, which includes the total selling price and the installation charge:
\[ \text{Total Amount Earned} = \text{Total Selling Price} + \text{Total Installation Charge} \]
\[ 402984 = 12.312P + 9000 \]

### Step 8: Solve for P
Now, we can isolate \( P \):
\[ 402984 - 9000 = 12.312P \]
\[ 393984 = 12.312P \]
\[ P = \frac{393984}{12.312} \]
Calculating this gives:
\[ P \approx 32000 \]

### Conclusion
The original price of one P model computer is Rs. 32000.