An agent sold a car and charged 3% commission on sale value. If the owner of the car received Rs.48,500, find the sale value of the car. If the agent charged 2% from the buyer, find his total remuneration.

Answer

To solve the problem step by step, we will follow the logical flow of the situation described.

### Step 1: Define the Sale Value
Let the sale value of the car be Rs. X.

### Step 2: Calculate the Commission Charged by the Agent from the Seller
The agent charges a 3% commission on the sale value. Therefore, the commission charged by the agent from the seller is:
\[ \text{Commission from seller} = 3\% \text{ of } X = \frac{3}{100} \times X = 0.03X \]

### Step 3: Calculate the Amount Received by the Owner
The amount received by the owner of the car is equal to the sale value minus the commission charged by the agent. Thus, we can write:
\[ \text{Amount received by owner} = X - 0.03X = 0.97X \]
According to the problem, the owner received Rs. 48,500. Therefore, we can set up the equation:
\[ 0.97X = 48500 \]

### Step 4: Solve for X (Sale Value)
To find the sale value X, we rearrange the equation:
\[ X = \frac{48500}{0.97} \]
Calculating this gives:
\[ X = 50000 \]
Thus, the sale value of the car is Rs. 50,000.

### Step 5: Calculate the Commission Charged by the Agent from the Buyer
The agent also charges a 2% commission from the buyer. Therefore, the commission charged by the agent from the buyer is:
\[ \text{Commission from buyer} = 2\% \text{ of } X = \frac{2}{100} \times 50000 = 1000 \]

### Step 6: Calculate the Commission Charged by the Agent from the Seller
We already calculated the commission charged by the agent from the seller:
\[ \text{Commission from seller} = 3\% \text{ of } X = \frac{3}{100} \times 50000 = 1500 \]

### Step 7: Calculate Total Remuneration of the Agent
The total remuneration of the agent is the sum of the commissions from the buyer and the seller:
\[ \text{Total remuneration} = \text{Commission from buyer} + \text{Commission from seller} = 1000 + 1500 = 2500 \]

### Final Answer
The total remuneration of the agent is Rs. 2500.

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