Three cars were sold through an agent for Rs.2,40,000 , Rs.2,22,000 and Rs.2,25,000 respectively. The rates of commission were 17.5% on the first, 12.5% on the second. If the agent overall received 14% commission on the total sales, find the rate of commission paid on the third car.

Answer

To solve the problem step by step, we will first calculate the total selling price of the three cars, then find the commission for each car, and finally determine the commission rate for the third car.

### Step 1: Calculate the total selling price of the three cars.
The selling prices of the cars are:
- First car: Rs. 2,40,000
- Second car: Rs. 2,22,000
- Third car: Rs. 2,25,000

Total selling price (TSP) = Selling price of first car + Selling price of second car + Selling price of third car

\[ \text{TSP} = 2,40,000 + 2,22,000 + 2,25,000 = 6,87,000 \]

### Step 2: Calculate the commission on the first car.
The commission rate for the first car is 17.5%.

\[ \text{Commission on first car (C1)} = 17.5\% \text{ of } 2,40,000 = \frac{17.5}{100} \times 2,40,000 = 42,000 \]

### Step 3: Calculate the commission on the second car.
The commission rate for the second car is 12.5%.

\[ \text{Commission on second car (C2)} = 12.5\% \text{ of } 2,22,000 = \frac{12.5}{100} \times 2,22,000 = 27,750 \]

### Step 4: Calculate the total commission received by the agent.
The overall commission rate is 14% of the total sales.

\[ \text{Total commission (C)} = 14\% \text{ of } 6,87,000 = \frac{14}{100} \times 6,87,000 = 96,180 \]

### Step 5: Set up the equation for the commission on the third car.
Let the commission rate for the third car be \( X\% \). The commission on the third car (C3) can be expressed as:

\[ \text{C3} = \frac{X}{100} \times 2,25,000 \]

### Step 6: Write the equation for total commission.
The total commission is the sum of the commissions from all three cars:

\[ C1 + C2 + C3 = C \]

Substituting the values we have:

\[ 42,000 + 27,750 + \frac{X}{100} \times 2,25,000 = 96,180 \]

### Step 7: Solve for \( X \).
First, combine the known commissions:

\[ 42,000 + 27,750 = 69,750 \]

Now substitute back into the equation:

\[ 69,750 + \frac{X}{100} \times 2,25,000 = 96,180 \]

Subtract 69,750 from both sides:

\[ \frac{X}{100} \times 2,25,000 = 96,180 - 69,750 \]

Calculating the right side:

\[ \frac{X}{100} \times 2,25,000 = 26,430 \]

Now, multiply both sides by 100:

\[ X \times 2,25,000 = 26,430 \times 100 \]

\[ X \times 2,25,000 = 2,643,000 \]

Now divide both sides by 2,25,000 to find \( X \):

\[ X = \frac{2,643,000}{2,25,000} = 11.75 \]

### Conclusion
The rate of commission paid on the third car is **11.75%**.

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