For Rs 25,500 a furniture shop sells 3 computer tables and 5 chairs OR 2 computer table and 9 chairs. If one wants to buy a set of only I computer table and 1 chair, how much does he need to pay?

Options

A. Rs 1,500
B. Rs 5,100
C. Rs 6,000
D. Rs 7,500

Answer

To solve the problem, we need to find the cost of one computer table and one chair based on the information given. Let's break it down step by step.

### Step 1: Set up the equations
Let the cost of one computer table be \( x \) and the cost of one chair be \( y \).

According to the problem, we have two scenarios:
1. For 3 computer tables and 5 chairs, the total cost is Rs 25,500:
\[ 3x + 5y = 25,500 \quad \text{(Equation 1)} \]

2. For 2 computer tables and 9 chairs, the total cost is also Rs 25,500:
\[ 2x + 9y = 25,500 \quad \text{(Equation 2)} \]

### Step 2: Solve the equations
We can solve these two equations simultaneously. Let's first multiply Equation 1 by 2 and Equation 2 by 3 to eliminate \( x \):

- Multiplying Equation 1 by 2:
\[ 2(3x + 5y) = 2(25,500) \implies 6x + 10y = 51,000 \quad \text{(Equation 3)} \]

- Multiplying Equation 2 by 3:
\[ 3(2x + 9y) = 3(25,500) \implies 6x + 27y = 76,500 \quad \text{(Equation 4)} \]

### Step 3: Subtract the equations
Now, we will subtract Equation 3 from Equation 4 to eliminate \( x \):
\[ (6x + 27y) - (6x + 10y) = 76,500 - 51,000 \]
This simplifies to:
\[ 17y = 25,500 \]

### Step 4: Solve for \( y \)
Now, divide both sides by 17 to find \( y \):
\[ y = \frac{25,500}{17} = 1,500 \]

### Step 5: Substitute \( y \) back to find \( x \)
Now that we have \( y \), we can substitute it back into Equation 1 to find \( x \):
\[ 3x + 5(1,500) = 25,500 \]
This simplifies to:
\[ 3x + 7,500 = 25,500 \]
Subtract 7,500 from both sides:
\[ 3x = 25,500 - 7,500 = 18,000 \]
Now, divide by 3:
\[ x = \frac{18,000}{3} = 6,000 \]

### Step 6: Find the total cost of 1 computer table and 1 chair
Now we have both \( x \) and \( y \):
- Cost of 1 computer table \( x = 6,000 \)
- Cost of 1 chair \( y = 1,500 \)

Thus, the total cost for 1 computer table and 1 chair is:
\[ x + y = 6,000 + 1,500 = 7,500 \]

### Final Answer
The total amount needed to pay for 1 computer table and 1 chair is Rs 7,500.

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