8 chairs and 5 tables cost Rs 10500, while 5 chairs and 3 tables cost Rs 6450. The cost of each chair will be:

Options

A. Rs 750
B. Rs 600
C. Rs 850
D. Rs 9000

Answer

To solve the problem step by step, we will set up equations based on the information provided and then solve those equations to find the cost of each chair.

### Step 1: Define Variables
Let the cost of one chair be Rs. \( x \) and the cost of one table be Rs. \( y \).

### Step 2: Set Up Equations
From the problem statement, we have two pieces of information that we can convert into equations:
1. For 8 chairs and 5 tables costing Rs. 10,500:
\[ 8x + 5y = 10500 \quad \text{(Equation 1)} \]
2. For 5 chairs and 3 tables costing Rs. 6,450:
\[ 5x + 3y = 6450 \quad \text{(Equation 2)} \]

### Step 3: Eliminate One Variable
To solve these equations, we can use the elimination method. We will eliminate \( y \) by making the coefficients of \( y \) in both equations equal.

Multiply Equation 1 by 3:
\[ 3(8x + 5y) = 3(10500) \implies 24x + 15y = 31500 \quad \text{(Equation 3)} \]

Multiply Equation 2 by 5:
\[ 5(5x + 3y) = 5(6450) \implies 25x + 15y = 32250 \quad \text{(Equation 4)} \]

### Step 4: Subtract the Equations
Now, we will subtract Equation 4 from Equation 3:
\[ (24x + 15y) - (25x + 15y) = 31500 - 32250 \]
This simplifies to:
\[ -1x = -750 \]
Thus, we find:
\[ x = 750 \]

### Step 5: Find the Cost of Each Chair
Now that we have the value of \( x \) (the cost of one chair), we can conclude that:
\[ \text{Cost of each chair} = Rs. 750 \]

### Step 6: (Optional) Find the Cost of Each Table
To find the cost of each table \( y \), we can substitute \( x = 750 \) back into either of the original equations. Let's use Equation 1:
\[ 8(750) + 5y = 10500 \]
This simplifies to:
\[ 6000 + 5y = 10500 \]
Subtracting 6000 from both sides gives:
\[ 5y = 4500 \]
Dividing by 5 gives:
\[ y = 900 \]

### Final Answer
The cost of each chair is Rs. 750.