Dipesh makes a profit of rupees Rs 120 if he sells certain number of pencils at the price of rupees 2.5 per pencil and incurs a loss of rupees 62, if he sells the same number of pencils for rupees 1.85 per pencil. How many pencils does Dipesh have ?

Options

A. 260
B. 280
C. 300
D. 320

Answer

To solve the problem step by step, we will define the variables and set up equations based on the information given in the question.

### Step-by-Step Solution:

1. **Define the Variables:**
Let \( N \) be the number of pencils Dipesh has.

2. **Selling Price and Profit:**
When Dipesh sells the pencils at Rs. 2.5 per pencil, he makes a profit of Rs. 120.
The total selling price in this case is:
\[ \text{Selling Price} = 2.5N \]
The cost price (CP) of the pencils can be expressed as:
\[ \text{Cost Price} = \text{Selling Price} - \text{Profit} = 2.5N - 120 \]

3. **Selling Price and Loss:**
When he sells the pencils at Rs. 1.85 per pencil, he incurs a loss of Rs. 62.
The total selling price in this case is:
\[ \text{Selling Price} = 1.85N \]
The cost price can also be expressed as:
\[ \text{Cost Price} = \text{Selling Price} + \text{Loss} = 1.85N + 62 \]

4. **Setting the Cost Prices Equal:**
Since both expressions represent the same cost price, we can set them equal to each other:
\[ 2.5N - 120 = 1.85N + 62 \]

5. **Solving the Equation:**
Rearranging the equation to isolate \( N \):
\[ 2.5N - 1.85N = 120 + 62 \]
\[ 0.65N = 182 \]
Now, divide both sides by 0.65 to find \( N \):
\[ N = \frac{182}{0.65} \]

6. **Calculating \( N \):**
To simplify the division, we can multiply the numerator and denominator by 100 to eliminate the decimal:
\[ N = \frac{182 \times 100}{65} = \frac{18200}{65} \]
Now, performing the division:
\[ N = 280 \]

### Final Answer:
Dipesh has **280 pencils**.