A man sells a table at 15% profit and chair at 12% loss and earn Rs 540 as profit. If he sel1 the table at 12% loss and chair at 15% profit then he bears no profit no loss. Find the price of table and chair.

Options

A. Rs 8000, Rs 10000
B. Rs 9000 Rs 7000
C. Rs 5000 Rs 8000
D. Rs 7000 Rs 9000

Answer

To solve the problem step by step, we will denote the cost price of the table as \( T \) and the cost price of the chair as \( C \).

### Step 1: Set up the equations based on the given information.

1. The man sells the table at a 15% profit:
\[ \text{Selling Price of Table} = T + 0.15T = 1.15T \]

2. He sells the chair at a 12% loss:
\[ \text{Selling Price of Chair} = C - 0.12C = 0.88C \]

3. The total profit from selling both items is Rs 540:
\[ 1.15T + 0.88C - (T + C) = 540 \]
Simplifying this gives:
\[ 0.15T - 0.12C = 540 \]
(Equation 1)

### Step 2: Set up the second scenario where he sells the table at a 12% loss and the chair at a 15% profit.

1. The selling price of the table at a 12% loss:
\[ \text{Selling Price of Table} = T - 0.12T = 0.88T \]

2. The selling price of the chair at a 15% profit:
\[ \text{Selling Price of Chair} = C + 0.15C = 1.15C \]

3. In this case, he bears no profit or loss:
\[ 0.88T + 1.15C - (T + C) = 0 \]
Simplifying this gives:
\[ -0.12T + 0.15C = 0 \]
Rearranging gives:
\[ 0.12T = 0.15C \]
(Equation 2)

### Step 3: Solve the equations simultaneously.

From Equation 2:
\[ \frac{T}{C} = \frac{0.15}{0.12} = \frac{5}{4} \]
This means:
\[ T = \frac{5}{4}C \]

### Step 4: Substitute \( T \) in Equation 1.

Substituting \( T \) in Equation 1:
\[ 0.15\left(\frac{5}{4}C\right) - 0.12C = 540 \]
This simplifies to:
\[ \frac{15}{4}C - 0.12C = 540 \]
Converting \( 0.12C \) to a fraction:
\[ 0.12C = \frac{12}{100}C = \frac{3}{25}C \]

Now, finding a common denominator (100):
\[ \frac{15}{4}C = \frac{375}{100}C \]
\[ \frac{3}{25}C = \frac{12}{100}C \]

Now substituting:
\[ \frac{375}{100}C - \frac{12}{100}C = 540 \]
\[ \frac{363}{100}C = 540 \]
Multiplying both sides by 100:
\[ 363C = 54000 \]
Dividing both sides by 363:
\[ C = \frac{54000}{363} \approx 148.68 \]

### Step 5: Find the price of the table \( T \).

Using \( T = \frac{5}{4}C \):
\[ T = \frac{5}{4} \times 148.68 \approx 185.85 \]

### Final Prices:
- Price of the Chair \( C \approx 148.68 \)
- Price of the Table \( T \approx 185.85 \)

### Summary:
The price of the table is approximately Rs 185.85 and the price of the chair is approximately Rs 148.68.