Vishal buys an old bike for Rs. 4700 and spends Rs. 800 on its repairs, then he sells it for Rs. 5800. Find his gain percent.

Options

A. `5.2%`
B. `4 (4)/(7)%`
C. `5%`
D. `5 (5)/(11)%`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the Total Cost Price (CP)
Vishal buys the bike for Rs. 4700 and spends Rs. 800 on repairs. Therefore, the total cost price (CP) is calculated as follows:

\[ \text{Total CP} = \text{Cost of bike} + \text{Repair cost} = 4700 + 800 = 5500 \]

### Step 2: Identify the Selling Price (SP)
Vishal sells the bike for Rs. 5800. Thus, the selling price (SP) is:

\[ \text{SP} = 5800 \]

### Step 3: Calculate the Gain
Gain is calculated by subtracting the total cost price from the selling price:

\[ \text{Gain} = \text{SP} - \text{CP} = 5800 - 5500 = 300 \]

### Step 4: Calculate the Gain Percent
Gain percent is calculated using the formula:

\[ \text{Gain Percent} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100 \]

Substituting the values we have:

\[ \text{Gain Percent} = \left( \frac{300}{5500} \right) \times 100 \]

### Step 5: Simplify the Gain Percent Calculation
First, simplify the fraction:

\[ \frac{300}{5500} = \frac{300 \div 100}{5500 \div 100} = \frac{3}{55} \]

Now, multiply by 100:

\[ \text{Gain Percent} = \frac{3}{55} \times 100 = \frac{300}{55} \]

### Step 6: Further Simplify
Now, we can simplify \( \frac{300}{55} \):

\[ \frac{300}{55} = \frac{60}{11} \approx 5.4545 \]

So, the gain percent can be expressed as:

\[ \text{Gain Percent} = 5 \frac{5}{11} \% \]

### Final Answer
Thus, Vishal's gain percent is \( 5 \frac{5}{11} \% \).

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