Abhishek makes a profit of Rs.110, if he sells a certain number of pens he has at the price of Rs 2.5 per pen and incurs a loss of Rs55, if he sells the same number of pens for Rs1.75 per pen. How many pens does Abhishek have?

Options

A. 220
B. 240
C. 200
D. cannot be determined

Answer

To find the number of pens Abhishek has, we can set up the problem using the information given in the question. Let's break it down step by step.

### Step 1: Define Variables
Let:
- \( X \) = Cost Price (CP) of one pen
- \( Y \) = Total number of pens

### Step 2: Set Up Equations Based on Given Conditions
1. **Profit Condition**: When Abhishek sells the pens at Rs. 2.5 each, he makes a profit of Rs. 110.
- Selling Price (SP) = \( 2.5Y \)
- Profit = SP - CP
- Therefore, we can write the equation:
\[ 2.5Y - XY = 110 \quad \text{(Equation 1)} \]

2. **Loss Condition**: When he sells the pens at Rs. 1.75 each, he incurs a loss of Rs. 55.
- Selling Price (SP) = \( 1.75Y \)
- Loss = CP - SP
- Therefore, we can write the equation:
\[ XY - 1.75Y = 55 \quad \text{(Equation 2)} \]

### Step 3: Rearranging the Equations
From Equation 1:
\[ 2.5Y - XY = 110 \implies XY = 2.5Y - 110 \quad \text{(Rearranging)} \]

From Equation 2:
\[ XY - 1.75Y = 55 \implies XY = 1.75Y + 55 \quad \text{(Rearranging)} \]

### Step 4: Set the Two Expressions for XY Equal
Since both expressions equal \( XY \), we can set them equal to each other:
\[ 2.5Y - 110 = 1.75Y + 55 \]

### Step 5: Solve for Y
Now, we will solve for \( Y \):
1. Rearranging gives:
\[ 2.5Y - 1.75Y = 55 + 110 \]
\[ 0.75Y = 165 \]
2. Dividing both sides by 0.75:
\[ Y = \frac{165}{0.75} = 220 \]

### Conclusion
Thus, the total number of pens Abhishek has is \( Y = 220 \).