Price of a chair is greater than the price of a table by Rs. 400. If the price of 6 chairs and 6 tables is Rs. 4800, then by how much percent the price of a table is less than the price of a chair?

Options

A. `(200)/(3) %`
B. `25%`
C. `37 (1)/(2) %`
D. `(2)/(3)%`

Answer

Let's solve the problem step by step.

### Step 1: Define the variables
Let the price of the table be \( T \) (in Rs) and the price of the chair be \( C \) (in Rs).

### Step 2: Set up the equations
According to the problem:
1. The price of a chair is greater than the price of a table by Rs. 400:
\[ C = T + 400 \]
2. The total price of 6 chairs and 6 tables is Rs. 4800:
\[ 6C + 6T = 4800 \]

### Step 3: Simplify the second equation
We can simplify the second equation by dividing everything by 6:
\[ C + T = 800 \]

### Step 4: Substitute the first equation into the second
Now, substitute \( C \) from the first equation into the second equation:
\[ (T + 400) + T = 800 \]
This simplifies to:
\[ 2T + 400 = 800 \]

### Step 5: Solve for \( T \)
Subtract 400 from both sides:
\[ 2T = 400 \]
Now divide by 2:
\[ T = 200 \]

### Step 6: Find the price of the chair \( C \)
Now, substitute \( T \) back into the equation for \( C \):
\[ C = T + 400 = 200 + 400 = 600 \]

### Step 7: Calculate the percentage difference
Now we need to find by how much percent the price of the table is less than the price of the chair. The formula for percentage difference is:
\[ \text{Percentage} = \left( \frac{C - T}{C} \right) \times 100 \]
Substituting the values of \( C \) and \( T \):
\[ \text{Percentage} = \left( \frac{600 - 200}{600} \right) \times 100 = \left( \frac{400}{600} \right) \times 100 \]
Calculating this gives:
\[ \text{Percentage} = \left( \frac{2}{3} \right) \times 100 \approx 66.67\% \]

### Final Answer
The price of the table is approximately **66.67% less than the price of the chair**.

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