5 chairs and 4 tables together cost ₹ 5600, while 4 chairs and 3 tables together cost ₹ 4340. Find the cost of a chair and that of a table.

Answer

To solve the problem, we will set up a system of linear equations based on the information provided and then solve for the cost of a chair and a table.

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

### Step 2: Set up the equations
From the problem, we have two pieces of information:
1. The cost of 5 chairs and 4 tables is ₹5600.
2. The cost of 4 chairs and 3 tables is ₹4340.

We can express these as equations:
1. \( 5x + 4y = 5600 \) (Equation 1)
2. \( 4x + 3y = 4340 \) (Equation 2)

### Step 3: Multiply the equations to eliminate one variable
To eliminate one variable, we can multiply the equations by suitable numbers. We will multiply Equation 1 by 3 and Equation 2 by 4.

- Multiplying Equation 1 by 3:
\[ 3(5x + 4y) = 3(5600) \implies 15x + 12y = 16800 \quad \text{(Equation 3)} \]

- Multiplying Equation 2 by 4:
\[ 4(4x + 3y) = 4(4340) \implies 16x + 12y = 17360 \quad \text{(Equation 4)} \]

### Step 4: Subtract the equations
Now, we will subtract Equation 3 from Equation 4 to eliminate \( y \):
\[ (16x + 12y) - (15x + 12y) = 17360 - 16800 \]
This simplifies to:
\[ x = 560 \]

### Step 5: Substitute back to find \( y \)
Now that we have \( x \), we can substitute it back into one of the original equations to find \( y \). We will use Equation 1:
\[ 5(560) + 4y = 5600 \]
This simplifies to:
\[ 2800 + 4y = 5600 \]
Subtracting 2800 from both sides gives:
\[ 4y = 2800 \]
Dividing by 4:
\[ y = 700 \]

### Step 6: Conclusion
Thus, the cost of one chair is ₹560 and the cost of one table is ₹700.

### Final Answer:
- Cost of one chair = ₹560
- Cost of one table = ₹700