Two chain and three tables cost Rs. 1025 and three chairs and two tables cost Rs. 1100. What is the difference between the cost of one table and that of one chair?

Options

A. Rs. 75
B. Rs. 35
C. Cannot be determined
D. 125

Answer

To solve the problem step by step, we will first set up equations based on the information given and then solve for the costs of the chairs and tables.

### Step 1: Set up the equations
Let:
- C = cost of one chair
- T = cost of one table

From the problem, we have the following two equations:
1. \( 2C + 3T = 1025 \) (Equation 1)
2. \( 3C + 2T = 1100 \) (Equation 2)

### Step 2: Equalize the coefficients of C
To eliminate C, we can equalize the coefficients of C in both equations. We can do this by multiplying Equation 1 by 3 and Equation 2 by 2.

- Multiply Equation 1 by 3:
\[ 3(2C + 3T) = 3(1025) \]
\[ 6C + 9T = 3075 \] (Equation 3)

- Multiply Equation 2 by 2:
\[ 2(3C + 2T) = 2(1100) \]
\[ 6C + 4T = 2200 \] (Equation 4)

### Step 3: Subtract the equations
Now, we will subtract Equation 4 from Equation 3 to eliminate C.

\[ (6C + 9T) - (6C + 4T) = 3075 - 2200 \]
This simplifies to:
\[ 5T = 875 \]

### Step 4: Solve for T
Now, we can solve for T:
\[ T = \frac{875}{5} \]
\[ T = 175 \]

### Step 5: Substitute T back to find C
Now that we have the cost of one table (T), we can substitute this value back into one of the original equations to find the cost of one chair (C). We will use Equation 1.

\[ 2C + 3(175) = 1025 \]
\[ 2C + 525 = 1025 \]
Now, subtract 525 from both sides:
\[ 2C = 1025 - 525 \]
\[ 2C = 500 \]
Now, divide by 2:
\[ C = \frac{500}{2} \]
\[ C = 250 \]

### Step 6: Find the difference
Now we need to find the difference between the cost of one table and one chair:
\[ \text{Difference} = C - T = 250 - 175 = 75 \]

### Final Answer
The difference between the cost of one table and that of one chair is **75 rupees**.

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