Anna sold his car to Boney at a profit of 20% and Boney sold it to Chakori at a profit of 10%. Chakori sold it to mechanic at a loss of 9.09%. Mechanic spent 10% of his purchasing price and then sold it at a prifit of 8.33% to Anna once again. What is the loss of Anna?

Options

A. 23%
B. 29%
C. 50%
D. 40%

Answer

To solve the problem step by step, let's break down the transactions involving Anna, Boney, Chakori, and the mechanic.

### Step 1: Anna sells the car to Boney
- Let the cost price (CP) of the car for Anna be \(100\) rupees.
- Anna sells the car to Boney at a profit of \(20\%\).
- Selling Price (SP) for Anna = CP + Profit = \(100 + (20\% \text{ of } 100) = 100 + 20 = 120\) rupees.

### Step 2: Boney sells the car to Chakori
- Boney bought the car for \(120\) rupees.
- Boney sells the car to Chakori at a profit of \(10\%\).
- Selling Price (SP) for Boney = CP + Profit = \(120 + (10\% \text{ of } 120) = 120 + 12 = 132\) rupees.

### Step 3: Chakori sells the car to the mechanic
- Chakori sold the car to the mechanic at a loss of \(9.09\%\).
- Loss percentage of \(9.09\%\) can be expressed as a fraction: \(9.09\% = \frac{1}{11}\).
- Selling Price (SP) for Chakori = CP - Loss = \(132 - (9.09\% \text{ of } 132) = 132 - \frac{1}{11} \times 132 = 132 \times \frac{10}{11} = 120\) rupees.

### Step 4: Mechanic spends on the car
- The mechanic bought the car for \(120\) rupees.
- The mechanic spends \(10\%\) of his purchasing price on the car.
- Amount spent = \(10\% \text{ of } 120 = 12\) rupees.
- Total cost for the mechanic = Purchase Price + Amount spent = \(120 + 12 = 132\) rupees.

### Step 5: Mechanic sells the car to Anna
- The mechanic sells the car at a profit of \(8.33\%\).
- Selling Price (SP) for the mechanic = CP + Profit = \(132 + (8.33\% \text{ of } 132) = 132 + 11 = 143\) rupees.

### Step 6: Calculate the loss for Anna
- Anna originally sold the car for \(120\) rupees and bought it back for \(143\) rupees.
- Loss for Anna = Buying Price - Selling Price = \(143 - 120 = 23\) rupees.

### Step 7: Calculate the percentage loss for Anna
- Percentage Loss = \(\frac{\text{Loss}}{\text{Original Cost Price}} \times 100 = \frac{23}{100} \times 100 = 23\%\).

### Final Answer
The loss of Anna is \(23\%\).

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