A shopkeeper sells a car for Rs.52510 and incurs a loss of 11%. He sells another car at 5% profit. If on selling both the cars he neither earns profit nor incurs loss, then find the cost price of second car.

Options

A. Rs 128300
B. Rs 129800
C. Rs 127400
D. Rs 126800

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Calculate the Cost Price of the First Car
The shopkeeper sells the first car for Rs. 52510 and incurs a loss of 11%.

Let the cost price (CP) of the first car be \( CP_1 \).

Using the formula for selling price (SP) when there is a loss:
\[ SP = CP \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]
We can rearrange this to find the cost price:
\[ CP_1 = \frac{SP}{1 - \frac{\text{Loss \%}}{100}} = \frac{52510}{1 - 0.11} = \frac{52510}{0.89} \]

Calculating this gives:
\[ CP_1 = 52510 \div 0.89 \approx 59000 \]

### Step 2: Calculate the Loss Incurred on the First Car
The loss incurred on the first car can be calculated as:
\[ \text{Loss} = CP_1 - SP = 59000 - 52510 = 6490 \]

### Step 3: Set Up the Equation for the Second Car
Let the cost price of the second car be \( CP_2 \). The selling price of the second car, sold at a profit of 5%, can be calculated as:
\[ SP_2 = CP_2 \times \left(1 + \frac{5}{100}\right) = CP_2 \times 1.05 \]

### Step 4: Total Profit/Loss from Both Cars
According to the problem, the shopkeeper neither earns profit nor incurs loss from selling both cars. Therefore, the total loss from the first car must equal the profit from the second car:
\[ \text{Loss from first car} = \text{Profit from second car} \]
Substituting the values we have:
\[ 6490 = SP_2 - CP_2 \]
Substituting \( SP_2 \):
\[ 6490 = (CP_2 \times 1.05) - CP_2 \]
This simplifies to:
\[ 6490 = 0.05 \times CP_2 \]

### Step 5: Solve for \( CP_2 \)
Now, we can solve for \( CP_2 \):
\[ CP_2 = \frac{6490}{0.05} = 6490 \times 20 = 129800 \]

### Final Answer
The cost price of the second car is Rs. 129800.

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