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 `₹2,42,125` by selling computers of type Q to a customer. The showroom transported the item to the customer and installed the computers. the sales tax is 10% what is original price of one Q model computer if customer purchased 9 computers from showroom

Options

A. `₹19,000`
B. `₹22,000`
C. `₹25,000`
D. `₹29,000`

Answer

To find the original price of one Q model computer, we will follow these steps:

### Step 1: Define Variables
Let the original price of computer P be \( P \). Then, we can express the prices of the other computers in terms of \( P \):
- Price of Q = \( P + 0.1P = 1.1P \)
- Price of R = \( Q + 0.12Q = 1.12 \times 1.1P = 1.232P \)
- Price of S = \( R - 0.1R = 0.9 \times 1.232P = 1.1088P \)

### Step 2: Calculate the Discounted Price of Q
The showroom offers a 5% discount on all purchases. Therefore, the discounted price of Q is:
\[ \text{Discounted Price of Q} = 1.1P \times (1 - 0.05) = 1.1P \times 0.95 = 1.045P \]

### Step 3: Calculate the Total Selling Price for 9 Computers
The customer purchased 9 computers of type Q, so the total price before tax is:
\[ \text{Total Price before Tax} = 9 \times 1.045P = 9.405P \]

### Step 4: Calculate the Total Charges
The showroom charges a delivery fee of ₹250 and an installation fee of ₹750 per computer. Therefore, for 9 computers, the installation charge is:
\[ \text{Installation Charge} = 9 \times 750 = 6750 \]
Thus, the total charges including delivery and installation is:
\[ \text{Total Charges} = 9.405P + 250 + 6750 = 9.405P + 7000 \]

### Step 5: Calculate the Total Amount Earned by the Showroom
The total amount earned by the showroom is given as ₹2,42,125. Thus, we can set up the equation:
\[ 9.405P + 7000 = 242125 \]

### Step 6: Solve for P
Subtract 7000 from both sides:
\[ 9.405P = 242125 - 7000 = 235125 \]
Now, divide both sides by 9.405:
\[ P = \frac{235125}{9.405} \approx 25000 \]

### Step 7: Find the Original Price of Q
Since the original price of Q is \( 1.1P \):
\[ \text{Original Price of Q} = 1.1 \times 25000 = 27500 \]

### Final Answer
The original price of one Q model computer is ₹27,500.

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