A man buys a table and a chair for Rs.500.He sells the table at a loss of 10% and the chair at a gain of 10%. He still gains Rs. 10 on the whole. The cost price of chair in rupees is

Options

A. a)Rs 200
B. b)Rs 250
C. c)Rs 300
D. d)Rs 350

Answer

To solve the problem, we need to find the cost price of the chair. Let's denote the cost price of the table as \( T \) and the cost price of the chair as \( C \). We know the following:

1. The total cost price of the table and chair is \( T + C = 500 \) (Equation 1).
2. The table is sold at a loss of 10%, so the selling price of the table is \( T - 0.1T = 0.9T \).
3. The chair is sold at a gain of 10%, so the selling price of the chair is \( C + 0.1C = 1.1C \).
4. The total selling price of both items results in a gain of Rs. 10 on the whole transaction, so we can write the equation for the total selling price as:
\[ 0.9T + 1.1C = 500 + 10 = 510 \quad \text{(Equation 2)} \]

Now, we can solve these equations step by step.

### Step 1: Express \( T \) in terms of \( C \)
From Equation 1, we have:
\[ T = 500 - C \]

### Step 2: Substitute \( T \) in Equation 2
Now, substitute \( T \) in Equation 2:
\[ 0.9(500 - C) + 1.1C = 510 \]

### Step 3: Simplify the equation
Distributing \( 0.9 \):
\[ 450 - 0.9C + 1.1C = 510 \]
Combine like terms:
\[ 450 + 0.2C = 510 \]

### Step 4: Isolate \( C \)
Subtract 450 from both sides:
\[ 0.2C = 510 - 450 \]
\[ 0.2C = 60 \]

### Step 5: Solve for \( C \)
Now, divide both sides by 0.2:
\[ C = \frac{60}{0.2} = 300 \]

### Conclusion
The cost price of the chair is Rs. 300.