A car mechanic purchased four old cars for ₹ 1 lakh. He spent total 2. lakh in the maintenance and repairing of these four cars. What is the average sale price of the rest three cars to get `50%` total profit if he has already sold one of the four cars at ₹ 1.2 lakh?

Options

A. 1.5 lakh
B. 1.1 lakh
C. 1.2 lakh
D. 1.65 lakh

Answer

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

### Step 1: Calculate the Total Cost Price
The mechanic purchased 4 old cars for ₹1 lakh and spent an additional ₹2 lakhs on maintenance and repairs.

\[ \text{Total Cost Price (CP)} = \text{Purchase Price} + \text{Maintenance Cost} = 1,00,000 + 2,00,000 = 3,00,000 \text{ (₹)} \]

**Hint:** Add the purchase price of the cars to the maintenance costs to find the total cost.

### Step 2: Calculate the Desired Selling Price for 50% Profit
To find the total selling price needed for a 50% profit, we first calculate the profit amount.

\[ \text{Desired Profit} = 50\% \text{ of Total CP} = 0.5 \times 3,00,000 = 1,50,000 \text{ (₹)} \]

Now, add this profit to the total cost price to find the total selling price.

\[ \text{Total Selling Price (SP)} = \text{Total CP} + \text{Desired Profit} = 3,00,000 + 1,50,000 = 4,50,000 \text{ (₹)} \]

**Hint:** To find the total selling price for a desired profit, calculate the profit amount based on the total cost and add it to the total cost.

### Step 3: Calculate the Selling Price of the Remaining Cars
The mechanic has already sold one of the four cars for ₹1.2 lakhs. We need to find out how much he needs to earn from the remaining three cars.

\[ \text{Remaining Selling Price} = \text{Total SP} - \text{Selling Price of the Sold Car} = 4,50,000 - 1,20,000 = 3,30,000 \text{ (₹)} \]

**Hint:** Subtract the selling price of the car that has already been sold from the total selling price to find out how much needs to be earned from the remaining cars.

### Step 4: Calculate the Average Selling Price of the Remaining Cars
To find the average selling price of the remaining three cars, divide the remaining selling price by the number of cars left.

\[ \text{Average Selling Price of Remaining Cars} = \frac{\text{Remaining Selling Price}}{\text{Number of Remaining Cars}} = \frac{3,30,000}{3} = 1,10,000 \text{ (₹)} \]

**Hint:** Divide the total amount needed from the remaining cars by the number of cars to find the average selling price.

### Final Answer
The average sale price of the rest three cars to achieve a 50% profit is ₹1,10,000.