3 chairs and 2 tables cost Rs. 700 while 5 chairs and 3 table cost Rs. 1100. What is the cost of 2 chairs and 2 table?

Answer

To solve the problem, we need to set up simultaneous equations based on the information given in the question.

### Step 1: Define the Variables
Let:
- \( x \) = cost of one chair
- \( y \) = cost of one table

### Step 2: Set Up the Equations
From the information provided:
1. The cost of 3 chairs and 2 tables is Rs. 700:
\[ 3x + 2y = 700 \quad \text{(Equation 1)} \]
2. The cost of 5 chairs and 3 tables is Rs. 1100:
\[ 5x + 3y = 1100 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
We will use the method of elimination to solve these equations. First, we can multiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of \( y \) the same:

- Multiply Equation 1 by 3:
\[ 9x + 6y = 2100 \quad \text{(Equation 3)} \]

- Multiply Equation 2 by 2:
\[ 10x + 6y = 2200 \quad \text{(Equation 4)} \]

### Step 4: Subtract the Equations
Now, subtract Equation 3 from Equation 4:
\[ (10x + 6y) - (9x + 6y) = 2200 - 2100 \]
This simplifies to:
\[ x = 100 \]

### Step 5: Substitute Back to Find \( y \)
Now that we have \( x \), we can substitute it back into Equation 1 to find \( y \):
\[ 3(100) + 2y = 700 \]
This simplifies to:
\[ 300 + 2y = 700 \]
Subtract 300 from both sides:
\[ 2y = 400 \]
Now divide by 2:
\[ y = 200 \]

### Step 6: Find the Cost of 2 Chairs and 2 Tables
Now we need to find the cost of 2 chairs and 2 tables:
\[ 2x + 2y = 2(100) + 2(200) \]
This simplifies to:
\[ 200 + 400 = 600 \]

### Final Answer
The cost of 2 chairs and 2 tables is Rs. 600.

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