Naveen purchased a gas cylinder and a stove for Rs.4500. He sold the gas cylinder at a gain of 25% and the stove at a loss of 20%, still gaining 4% on the whole. Find the cost of the gas cylinder.
A. Rs.3600
B. Rs.2400
C. Rs.3000
D. Rs.2600

Options

A. A
B. D
C. C
D. B

Answer

To solve the problem, we need to determine the cost of the gas cylinder that Naveen purchased. Let's denote the cost of the gas cylinder as \( x \) and the cost of the stove as \( y \). According to the problem, we know the following:

1. The total cost of the gas cylinder and stove is Rs. 4500:
\[ x + y = 4500 \]

2. The gas cylinder is sold at a gain of 25%, so the selling price of the gas cylinder is:
\[ \text{Selling Price of Gas Cylinder} = x + 0.25x = 1.25x \]

3. The stove is sold at a loss of 20%, so the selling price of the stove is:
\[ \text{Selling Price of Stove} = y - 0.20y = 0.80y \]

4. The overall gain on the total purchase is 4%, which means the total selling price of both items is:
\[ \text{Total Selling Price} = 4500 + 0.04 \times 4500 = 4500 + 180 = 4680 \]

Now we can set up the equation for the total selling price:
\[ 1.25x + 0.80y = 4680 \]

Now we have a system of equations:
1. \( x + y = 4500 \) (Equation 1)
2. \( 1.25x + 0.80y = 4680 \) (Equation 2)

### Step 1: Solve Equation 1 for \( y \)
From Equation 1, we can express \( y \) in terms of \( x \):
\[ y = 4500 - x \]

### Step 2: Substitute \( y \) in Equation 2
Now substitute \( y \) in Equation 2:
\[ 1.25x + 0.80(4500 - x) = 4680 \]

### Step 3: Simplify the equation
Expanding the equation:
\[ 1.25x + 3600 - 0.80x = 4680 \]
Combine like terms:
\[ (1.25 - 0.80)x + 3600 = 4680 \]
\[ 0.45x + 3600 = 4680 \]

### Step 4: Isolate \( x \)
Subtract 3600 from both sides:
\[ 0.45x = 4680 - 3600 \]
\[ 0.45x = 1080 \]

### Step 5: Solve for \( x \)
Now divide both sides by 0.45:
\[ x = \frac{1080}{0.45} = 2400 \]

Thus, the cost of the gas cylinder is Rs. 2400.

### Final Answer:
The cost of the gas cylinder is Rs. 2400 (Option B).

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