Amar sold his moped to Bharat at 20% profit and Bharat sold it to Sridhar at 10% profit. Sridhar sold the same to a mechanic and received Rs. 2,316. If Amar had sold the same moped to the mechanic and receive the same amount the mechanic paid to Sridhar, what profit percentage would Amar have made?

Options

A. `52%`
B. `48%`
C. `33.3%`
D. Cannot be determined

Answer

To solve the problem, we need to find out what profit percentage Amar would have made if he sold the moped directly to the mechanic for Rs. 2,316. Let's break it down step by step.

### Step 1: Determine the selling price of the moped for Sridhar
Sridhar sold the moped to the mechanic for Rs. 2,316.

### Step 2: Calculate the cost price of the moped for Sridhar
Sridhar sold the moped at a 10% profit. Let the cost price of the moped for Sridhar be \( CP_S \).

Using the formula for selling price:
\[ SP = CP + (Profit \% \times CP) \]
\[ 2316 = CP_S + (10\% \times CP_S) \]
\[ 2316 = CP_S + 0.1 \times CP_S \]
\[ 2316 = 1.1 \times CP_S \]

Now, we can solve for \( CP_S \):
\[ CP_S = \frac{2316}{1.1} = 2106 \]

### Step 3: Calculate the cost price of the moped for Bharat
Bharat sold the moped to Sridhar at a 10% profit. Let the cost price of the moped for Bharat be \( CP_B \).

Using the same formula:
\[ CP_S = CP_B + (20\% \times CP_B) \]
\[ 2106 = CP_B + 0.2 \times CP_B \]
\[ 2106 = 1.2 \times CP_B \]

Now, we can solve for \( CP_B \):
\[ CP_B = \frac{2106}{1.2} = 1755 \]

### Step 4: Calculate the cost price of the moped for Amar
Amar sold the moped to Bharat at a 20% profit. Let the cost price of the moped for Amar be \( CP_A \).

Using the same formula:
\[ CP_B = CP_A + (20\% \times CP_A) \]
\[ 1755 = CP_A + 0.2 \times CP_A \]
\[ 1755 = 1.2 \times CP_A \]

Now, we can solve for \( CP_A \):
\[ CP_A = \frac{1755}{1.2} = 1462.5 \]

### Step 5: Calculate the profit Amar would have made
If Amar sold the moped to the mechanic for Rs. 2,316, we can now calculate the profit he would have made.

Profit = Selling Price - Cost Price
\[ Profit = 2316 - 1462.5 = 853.5 \]

### Step 6: Calculate the profit percentage
Profit percentage can be calculated using the formula:
\[ Profit \% = \left( \frac{Profit}{Cost Price} \right) \times 100 \]
\[ Profit \% = \left( \frac{853.5}{1462.5} \right) \times 100 \approx 58.3\% \]

### Final Answer
If Amar had sold the moped to the mechanic for Rs. 2,316, he would have made a profit percentage of approximately **58.3%**.

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