By selling a cycle for र 2345, a student loses 19%. His cost price is nearly

Options

A. र 4000
B. र 5000
C. र 3000
D. र 3500

Answer

To find the cost price (CP) of the cycle when the selling price (SP) is Rs. 2345 and there is a loss of 19%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between Selling Price, Cost Price, and Loss Percentage:**
The formula to relate Selling Price (SP), Cost Price (CP), and Loss Percentage (Loss%) is:
\[ SP = CP \times (1 - \text{Loss%}) \]
In this case, Loss% is 19%, which can be expressed as a decimal:
\[ \text{Loss%} = \frac{19}{100} = 0.19 \]

2. **Substituting the values into the formula:**
Given that SP = Rs. 2345, we can substitute the values into the formula:
\[ 2345 = CP \times (1 - 0.19) \]
Simplifying the equation:
\[ 2345 = CP \times 0.81 \]

3. **Rearranging to find the Cost Price (CP):**
To find CP, we rearrange the equation:
\[ CP = \frac{2345}{0.81} \]

4. **Calculating the Cost Price:**
Now we perform the division:
\[ CP \approx \frac{2345}{0.81} \approx 2895.67 \]
Since the question asks for the cost price to be nearly, we can round this to the nearest whole number:
\[ CP \approx 2896 \]

5. **Final Answer:**
The cost price of the cycle is approximately Rs. 2896.