4 chairs and 3 tables cost Rs 2100 and 5 chairs and 2 tables cost Rs 1750. Find the cost of a chair and a table separately.

Answer

To solve the problem of finding the cost of a chair and a table separately, we can set up a system of linear equations based on the information provided.

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

### Step 2: Set Up Equations
From the problem, we have two pieces of information that we can turn into equations:

1. Four chairs and three tables cost Rs 2100:
\[ 4x + 3y = 2100 \quad \text{(Equation 1)} \]

2. Five chairs and two tables cost Rs 1750:
\[ 5x + 2y = 1750 \quad \text{(Equation 2)} \]

### Step 3: Solve the First Equation for One Variable
We can solve Equation 1 for \( x \):
\[ 4x + 3y = 2100 \]
Rearranging gives:
\[ 4x = 2100 - 3y \]
Dividing by 4:
\[ x = \frac{2100 - 3y}{4} \quad \text{(Equation 3)} \]

### Step 4: Substitute into the Second Equation
Now, substitute Equation 3 into Equation 2:
\[ 5\left(\frac{2100 - 3y}{4}\right) + 2y = 1750 \]
Multiplying through by 4 to eliminate the fraction:
\[ 5(2100 - 3y) + 8y = 7000 \]
Expanding:
\[ 10500 - 15y + 8y = 7000 \]
Combining like terms:
\[ 10500 - 7y = 7000 \]

### Step 5: Solve for \( y \)
Rearranging gives:
\[ -7y = 7000 - 10500 \]
\[ -7y = -3500 \]
Dividing by -7:
\[ y = 500 \]

### Step 6: Substitute \( y \) Back to Find \( x \)
Now that we have \( y \), substitute back into Equation 3 to find \( x \):
\[ x = \frac{2100 - 3(500)}{4} \]
Calculating:
\[ x = \frac{2100 - 1500}{4} = \frac{600}{4} = 150 \]

### Final Answer
The cost of a chair is Rs 150, and the cost of a table is Rs 500.

### Summary of Results
- Cost of a chair \( (x) = 150 \) Rs
- Cost of a table \( (y) = 500 \) Rs