When a bicycle manufacturer reduced its selling price by `50%`, the number of bicycles sold radically increased by `600%`. Initially the manufacturer was getting only `140%` profit. What is the percentage increase of his profit?

Options

A. `10%`
B. `14%`
C. `0%`
D. can’t be determined

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Initial Conditions
Let the cost price (CP) of one bicycle be \( CP \).

The initial selling price (SP) can be calculated based on the profit percentage. The manufacturer was getting a profit of \( 140\% \). This means:
\[ SP = CP + (140\% \text{ of } CP) = CP + 1.4 \times CP = 2.4 \times CP \]

### Step 2: Calculate the Initial Selling Price
Since we don't know the exact value of CP, we can express the initial selling price in terms of CP:
\[ SP = 2.4 \times CP \]

### Step 3: Determine the New Selling Price after Reduction
The manufacturer reduced the selling price by \( 50\% \). Therefore, the new selling price (SP') is:
\[ SP' = SP - (50\% \text{ of } SP) = SP - 0.5 \times SP = 0.5 \times SP \]
Substituting the expression for SP:
\[ SP' = 0.5 \times (2.4 \times CP) = 1.2 \times CP \]

### Step 4: Determine the Increase in Sales
The number of bicycles sold increased by \( 600\% \). This means if initially \( 1 \) bicycle was sold, now \( 7 \) bicycles are sold (1 original + 6 additional).

### Step 5: Calculate the Total Cost Price and Selling Price for 7 Bicycles
- Total cost price for 7 bicycles:
\[ \text{Total CP} = 7 \times CP \]
- Total selling price for 7 bicycles:
\[ \text{Total SP} = 7 \times SP' = 7 \times (1.2 \times CP) = 8.4 \times CP \]

### Step 6: Calculate the Profit
Profit can be calculated as:
\[ \text{Profit} = \text{Total SP} - \text{Total CP} = (8.4 \times CP) - (7 \times CP) = 1.4 \times CP \]

### Step 7: Calculate the Initial Profit
Initially, the profit was:
\[ \text{Initial Profit} = 1.4 \times CP \]

### Step 8: Calculate the Percentage Increase in Profit
Since the profit remains the same at \( 1.4 \times CP \), we can calculate the percentage increase in profit:
\[ \text{Percentage Increase} = \frac{\text{New Profit} - \text{Initial Profit}}{\text{Initial Profit}} \times 100\% \]
Since the new profit is equal to the initial profit:
\[ \text{Percentage Increase} = \frac{1.4 \times CP - 1.4 \times CP}{1.4 \times CP} \times 100\% = 0\% \]

### Final Answer
The percentage increase in profit is \( 0\% \).

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