The ratio of cost of table and chair is `9: 4`. The cost of table Is Rs. 1250 more than cost of chair. What Is the cost (in Rs.) of chair?

Options

A. 1000
B. 1200
C. 800
D. 1500

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the Variables
Let the cost of the table be represented as \( T \) and the cost of the chair as \( C \). According to the problem, the ratio of the cost of the table to the cost of the chair is given as \( 9:4 \).

### Step 2: Express Costs in Terms of a Variable
From the ratio \( 9:4 \), we can express the costs in terms of a variable \( x \):
- Cost of the table \( T = 9x \)
- Cost of the chair \( C = 4x \)

### Step 3: Set Up the Equation
According to the problem, the cost of the table is Rs. 1250 more than the cost of the chair. Therefore, we can set up the equation:
\[ T = C + 1250 \]
Substituting the expressions for \( T \) and \( C \):
\[ 9x = 4x + 1250 \]

### Step 4: Solve the Equation
Now, we will solve the equation for \( x \):
1. Rearranging the equation gives us:
\[ 9x - 4x = 1250 \]
2. Simplifying this, we get:
\[ 5x = 1250 \]
3. Dividing both sides by 5:
\[ x = \frac{1250}{5} = 250 \]

### Step 5: Calculate the Cost of the Chair
Now that we have the value of \( x \), we can find the cost of the chair:
\[ C = 4x = 4 \times 250 = 1000 \]

### Final Answer
Thus, the cost of the chair is Rs. 1000.

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