A cycle agent buys 30 bicycles, of which 8 are first grade and the rest are second grade for Rs. 3150. Find at what price he must sell the first grade bicycles so that if he sells the second grade bicycles at third quarter of the price, he may make a profit of 40% on both the types of transactions ?

Options

A. Rs. 200
B. Rs. 240
C. Rs. 180
D. Rs. 210

Answer

To solve the problem step by step, we will first determine the cost price and then calculate the selling price required to achieve a 40% profit.

### Step 1: Determine the Cost Price of Each Type of Bicycle
The agent buys a total of 30 bicycles for Rs. 3150. Out of these, 8 are first grade and the remaining (30 - 8 = 22) are second grade.

- Total cost price (CP) = Rs. 3150
- Number of first grade bicycles (A) = 8
- Number of second grade bicycles (B) = 22

### Step 2: Calculate the Total Selling Price for 40% Profit
To find the selling price (SP) needed for a 40% profit, we use the formula:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where:
\[ \text{Profit} = \text{CP} \times \frac{40}{100} \]

Calculating the profit:
\[ \text{Profit} = 3150 \times 0.4 = 1260 \]

Now, calculate the total selling price:
\[ \text{SP} = 3150 + 1260 = 4410 \]

### Step 3: Set Up the Selling Price Equation
Let the selling price of one first grade bicycle be Rs. n. The selling price of one second grade bicycle is given as three-quarters of the price of the first grade bicycle:
\[ \text{SP of second grade} = \frac{3n}{4} \]

Now, we can express the total selling price for both types of bicycles:
- Selling price of 8 first grade bicycles = \( 8n \)
- Selling price of 22 second grade bicycles = \( 22 \times \frac{3n}{4} = \frac{66n}{4} = 16.5n \)

### Step 4: Combine the Selling Prices
The total selling price for all bicycles can be expressed as:
\[ \text{Total SP} = 8n + 16.5n = 24.5n \]

### Step 5: Set the Total Selling Price Equal to Required Selling Price
We know from Step 2 that the total selling price must equal Rs. 4410:
\[ 24.5n = 4410 \]

### Step 6: Solve for n
To find the selling price of one first grade bicycle (n), we divide both sides by 24.5:
\[ n = \frac{4410}{24.5} \]

Calculating n:
\[ n = 180 \]

### Conclusion
The selling price of one first grade bicycle must be Rs. 180.

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