A man buys two tables at a total cost of T 480. If the loss on first table is 15% and the profit on second table is 19% and the S.P. of both tables are equal. Find the C.P.

Options

A. Rs 280 Rs 200
B. Rs 220 Rs 260
C. Rs 240 Rs 240
D. Rs 210 Rs 270

Answer

To solve the problem, let's break it down step by step.

### Step 1: Define Variables
Let the cost price (C.P.) of the first table be \( x \) and the cost price of the second table be \( y \).

### Step 2: Set Up the Equation for Total Cost
According to the problem, the total cost of both tables is T 480. Therefore, we can write:
\[ x + y = 480 \quad \text{(1)} \]

### Step 3: Calculate Selling Price of the First Table
The first table has a loss of 15%. The selling price (S.P.) can be calculated as:
\[ \text{S.P. of first table} = x - (15\% \text{ of } x) = x - 0.15x = 0.85x \]

### Step 4: Calculate Selling Price of the Second Table
The second table has a profit of 19%. The selling price can be calculated as:
\[ \text{S.P. of second table} = y + (19\% \text{ of } y) = y + 0.19y = 1.19y \]

### Step 5: Set Up the Equation for Equal Selling Prices
Since the selling prices of both tables are equal, we can set up the equation:
\[ 0.85x = 1.19y \quad \text{(2)} \]

### Step 6: Solve the System of Equations
Now we have a system of equations (1) and (2). We can solve for \( y \) in terms of \( x \) from equation (1):
\[ y = 480 - x \quad \text{(3)} \]

Substituting equation (3) into equation (2):
\[ 0.85x = 1.19(480 - x) \]

### Step 7: Expand and Rearrange
Expanding the right-hand side:
\[ 0.85x = 571.2 - 1.19x \]
Now, add \( 1.19x \) to both sides:
\[ 0.85x + 1.19x = 571.2 \]
\[ 2.04x = 571.2 \]

### Step 8: Solve for \( x \)
Now, divide both sides by 2.04 to find \( x \):
\[ x = \frac{571.2}{2.04} \approx 280 \]

### Step 9: Find \( y \)
Now, substitute \( x \) back into equation (3) to find \( y \):
\[ y = 480 - 280 = 200 \]

### Step 10: Conclusion
The cost price of the first table is T 280 and the cost price of the second table is T 200.