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

Answer

To solve the problem step by step, we will calculate the selling prices at each transaction and finally determine the loss incurred by Anna when she buys back her car.

### Step 1: Calculate the selling price of the car when Anna sells it to Boney.
Let the cost price of the car for Anna be \( CP_A \).

Anna sells the car to Boney at a profit of 20%.
So, the selling price (SP) for Boney is calculated as follows:
\[ SP_B = CP_A + (20\% \text{ of } CP_A) = CP_A \times (1 + 0.20) = CP_A \times 1.20 \]

### Step 2: Calculate the selling price of the car when Boney sells it to Chokori.
Boney sells the car to Chokori at a profit of 10%.
So, the selling price for Chokori is:
\[ SP_C = SP_B + (10\% \text{ of } SP_B) = SP_B \times (1 + 0.10) = SP_B \times 1.10 \]
Substituting \( SP_B \):
\[ SP_C = (CP_A \times 1.20) \times 1.10 = CP_A \times 1.20 \times 1.10 = CP_A \times 1.32 \]

### Step 3: Calculate the selling price of the car when Chokori sells it to the mechanic.
Chokori sells the car to the mechanic at a loss of 9.09%.
So, the selling price for the mechanic is:
\[ SP_M = SP_C - (9.09\% \text{ of } SP_C) = SP_C \times (1 - 0.0909) = SP_C \times 0.9091 \]
Substituting \( SP_C \):
\[ SP_M = (CP_A \times 1.32) \times 0.9091 = CP_A \times 1.32 \times 0.9091 \approx CP_A \times 1.20 \]

### Step 4: Calculate the selling price of the car when the mechanic sells it back to Anna.
The mechanic spends 10% of his purchasing price on repairs.
So, the cost price for the mechanic after repairs is:
\[ CP_M = SP_M + (10\% \text{ of } SP_M) = SP_M \times (1 + 0.10) = SP_M \times 1.10 \]
Substituting \( SP_M \):
\[ CP_M = (CP_A \times 1.20) \times 1.10 = CP_A \times 1.20 \times 1.10 = CP_A \times 1.32 \]

The mechanic sells it at a profit of 8.33%:
\[ SP_A = CP_M + (8.33\% \text{ of } CP_M) = CP_M \times (1 + 0.0833) = CP_M \times 1.0833 \]
Substituting \( CP_M \):
\[ SP_A = (CP_A \times 1.32) \times 1.0833 \approx CP_A \times 1.43 \]

### Step 5: Calculate the loss incurred by Anna.
Now we need to find the loss Anna incurred when she buys back the car:
\[ \text{Loss} = SP_A - CP_A \]
Substituting \( SP_A \):
\[ \text{Loss} = (CP_A \times 1.43) - CP_A = CP_A \times (1.43 - 1) = CP_A \times 0.43 \]

Thus, Anna incurs a loss of 43% of the original cost price of the car.

### Summary of Steps:
1. Calculate the selling price when Anna sells to Boney.
2. Calculate the selling price when Boney sells to Chokori.
3. Calculate the selling price when Chokori sells to the mechanic.
4. Calculate the selling price when the mechanic sells back to Anna.
5. Calculate the loss incurred by Anna.