By selling a bicycle for 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be

Options

A. 1. 2600
B. 2. 2700
C. 3. 2800
D. 4. 3000

Answer

To solve the problem step by step, we will first find the cost price of the bicycle using the information given about the selling price and the profit percentage. Then, we will calculate the new selling price when the profit percentage is reduced to 8%.

### Step 1: Find the Cost Price (CP)
The selling price (SP) is given as 2850, and the profit percentage is 14%.

Using the formula for selling price:
\[ SP = CP + \text{Profit} \]
Since profit is 14% of the cost price, we can express it as:
\[ \text{Profit} = 14\% \text{ of } CP = \frac{14}{100} \times CP \]
Thus, we can rewrite the selling price formula as:
\[ SP = CP + \frac{14}{100} \times CP \]
This simplifies to:
\[ SP = CP \left(1 + \frac{14}{100}\right) = CP \left(\frac{114}{100}\right) \]
Now, substituting the selling price:
\[ 2850 = CP \left(\frac{114}{100}\right) \]
To find the cost price (CP), we rearrange the equation:
\[ CP = 2850 \times \frac{100}{114} \]
Calculating this gives:
\[ CP = 2850 \times \frac{100}{114} \approx 2500 \]

### Step 2: Calculate the Selling Price for 8% Profit
Now that we have the cost price (CP) as 2500, we need to find the new selling price when the profit is reduced to 8%.

Using the profit formula again:
\[ \text{Profit} = 8\% \text{ of } CP = \frac{8}{100} \times 2500 \]
Calculating the profit:
\[ \text{Profit} = 0.08 \times 2500 = 200 \]

Now, we can find the new selling price (SP) with this profit:
\[ SP = CP + \text{Profit} = 2500 + 200 = 2700 \]

### Final Answer
The selling price when the profit is reduced to 8% will be **2700**.

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