To solve the problem step by step, let's break down the information given and calculate the total expenditure for company XY.
### Step 1: Calculate the price of Computer P
Given that the price of Computer R is ₹30,000, we first need to find the prices of Computers Q and P.
1. **Price of Q**:
- Price of Q is 10% more than P.
- Let the price of P be \( P \).
- Then, the price of Q = \( P + 0.1P = 1.1P \).
2. **Price of R**:
- Price of R is 12% more than Q.
- Price of R = \( Q + 0.12Q = 1.12Q \).
- Since the price of R is given as ₹30,000, we can set up the equation:
\[
1.12Q = 30,000 \implies Q = \frac{30,000}{1.12} \approx 26,785.71
\]
3. **Price of P**:
- Now substituting Q back to find P:
\[
1.1P = 26,785.71 \implies P = \frac{26,785.71}{1.1} \approx 24,793.37
\]
### Step 2: Calculate the price of Computer S
- The price of S is 10% less than R.
- Price of S = \( R - 0.1R = 0.9R \).
- Therefore:
\[
\text{Price of S} = 0.9 \times 30,000 = 27,000
\]
### Step 3: Calculate the discounted price of Computer S
- The showroom offers a 5% discount on all purchases before sales tax is calculated.
- Discount on S = 5% of 27,000 = \( 0.05 \times 27,000 = 1,350 \).
- Discounted price of S = \( 27,000 - 1,350 = 25,650 \).
### Step 4: Calculate the sales tax on the discounted price
- Sales tax is 10% of the discounted price.
- Sales tax = \( 0.10 \times 25,650 = 2,565 \).
- Final price after sales tax = \( 25,650 + 2,565 = 28,215 \).
### Step 5: Calculate the total cost for 12 computers
- Total cost for 12 computers = \( 12 \times 28,215 = 338,580 \).
### Step 6: Add transportation and installation charges
- Transportation charge = ₹250 (fixed for any number of computers).
- Installation charge = ₹750 per computer.
- Total installation charge for 12 computers = \( 12 \times 750 = 9,000 \).
### Step 7: Calculate the total expenditure
- Total expenditure = Cost of computers + Transportation charge + Installation charge
- Total expenditure = \( 338,580 + 250 + 9,000 = 347,830 \).
### Final Answer
The total amount spent by company XY is **₹347,830**.
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