Vishnu sells a bike at a profit of 5% for ₹ 10500. If the decreases the selling price to ₹ 9000,will he gain or lose and by how much percentage ?

Options

A. Gain, `15%`
B. Loss, `10%`
C. Loss, `15%`
D. Gain, `10%`

Explanation

To solve the problem step by step, we need to find out the cost price of the bike first, then determine the new selling price and calculate whether Vishnu gains or loses, along with the percentage of gain or loss.

### Step 1: Calculate the Cost Price (CP)
Given that Vishnu sells the bike at a selling price (SP) of ₹10,500 with a profit percentage of 5%, we can use the formula for selling price:

\[ SP = CP + \text{Profit} \]

The profit can also be expressed in terms of the cost price:

\[ \text{Profit} = \frac{5}{100} \times CP \]

Substituting this into the selling price formula gives us:

\[ SP = CP + \frac{5}{100} \times CP \]

This simplifies to:

\[ SP = CP \left(1 + \frac{5}{100}\right) = CP \left(\frac{105}{100}\right) \]

Now, substituting the selling price:

\[ 10,500 = CP \left(\frac{105}{100}\right) \]

To find the cost price (CP), we rearrange the equation:

\[ CP = 10,500 \times \frac{100}{105} \]

Calculating this gives:

\[ CP = 10,500 \times \frac{100}{105} = 10,000 \]

### Step 2: Determine the New Selling Price
The new selling price (SP) is given as ₹9,000.

### Step 3: Calculate Gain or Loss
Now we need to find out if Vishnu gains or loses by comparing the new selling price with the cost price:

- Cost Price (CP) = ₹10,000
- New Selling Price (SP) = ₹9,000

Since the new selling price is less than the cost price, Vishnu incurs a loss.

### Step 4: Calculate the Amount of Loss
The amount of loss can be calculated as:

\[ \text{Loss} = CP - SP = 10,000 - 9,000 = 1,000 \]

### Step 5: Calculate the Percentage of Loss
The percentage of loss can be calculated using the formula:

\[ \text{Percentage of Loss} = \left(\frac{\text{Loss}}{CP}\right) \times 100 \]

Substituting the values:

\[ \text{Percentage of Loss} = \left(\frac{1,000}{10,000}\right) \times 100 = 10\% \]

### Final Answer
Vishnu incurs a loss of ₹1,000, which is 10% of the cost price.

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