A car and a jeep were sold for Rs 120000 each. The car was sold at a loss of 20% while the jeep at a gain of 20%, the entire transaction resulted in:

Options

A. a)Neither loss nor gain
B. b)4% Gain
C. c)4% Loss
D. d)% Gain

Answer

To solve the problem step by step, we will analyze the situation involving the sale of a car and a jeep, both sold for Rs 120,000 each, with one sold at a loss and the other at a gain.

### Step 1: Understand the Selling Prices
Both the car and the jeep were sold for Rs 120,000 each.

### Step 2: Determine the Cost Price of the Car
The car was sold at a loss of 20%.
Let the cost price (CP) of the car be \( x \).
Since it was sold at a loss of 20%, the selling price (SP) can be expressed as:
\[ SP = CP - (20\% \text{ of } CP) = x - 0.2x = 0.8x \]
Given that the SP of the car is Rs 120,000:
\[ 0.8x = 120000 \]
To find \( x \):
\[ x = \frac{120000}{0.8} = 150000 \]
So, the cost price of the car is Rs 150,000.

### Step 3: Determine the Cost Price of the Jeep
The jeep was sold at a gain of 20%.
Let the cost price (CP) of the jeep be \( y \).
Since it was sold at a gain of 20%, the selling price (SP) can be expressed as:
\[ SP = CP + (20\% \text{ of } CP) = y + 0.2y = 1.2y \]
Given that the SP of the jeep is Rs 120,000:
\[ 1.2y = 120000 \]
To find \( y \):
\[ y = \frac{120000}{1.2} = 100000 \]
So, the cost price of the jeep is Rs 100,000.

### Step 4: Calculate the Total Cost Price
Now, we can calculate the total cost price (CP) of both the car and the jeep:
\[ \text{Total CP} = \text{CP of Car} + \text{CP of Jeep} = 150000 + 100000 = 250000 \]

### Step 5: Calculate the Total Selling Price
The total selling price (SP) of both the car and the jeep is:
\[ \text{Total SP} = \text{SP of Car} + \text{SP of Jeep} = 120000 + 120000 = 240000 \]

### Step 6: Determine Overall Profit or Loss
Now, we can determine if there was an overall profit or loss:
\[ \text{Total Profit or Loss} = \text{Total SP} - \text{Total CP} = 240000 - 250000 = -10000 \]
This indicates a loss of Rs 10,000.

### Step 7: Calculate the Loss Percentage
To find the loss percentage:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{\text{Total CP}}\right) \times 100 = \left(\frac{10000}{250000}\right) \times 100 = 4\% \]

### Final Answer
The entire transaction resulted in a loss of 4%.

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