A shopkeeper gains rs. 1 on each pen and loses 40 paise on each pencil. He sells 45 pens and some pencils losing Rs. 5 in all. How many pencils does he sell?

Answer

To solve the problem step by step, we will follow the given information and set up the equations accordingly.

### Step 1: Understand the Gains and Losses
- The shopkeeper gains Rs. 1 on each pen sold.
- The shopkeeper loses 40 paise (which is Rs. 0.40) on each pencil sold.

### Step 2: Calculate Total Gain from Pens
- The shopkeeper sells 45 pens.
- Gain from selling 45 pens = 45 pens × Rs. 1/pen = Rs. 45.

### Step 3: Set Up the Equation for Total Loss
- The total loss incurred by the shopkeeper is Rs. 5.
- Let the number of pencils sold be \( x \).
- Loss from selling \( x \) pencils = \( x \times 0.40 \) (since he loses Rs. 0.40 on each pencil).

### Step 4: Write the Total Gain and Loss Equation
- The total gain from pens minus the total loss from pencils should equal the overall loss:

\[ \text{Total Gain from Pens} - \text{Total Loss from Pencils} = \text{Total Loss} \]

Substituting the values we have:

\[ 45 - 0.40x = -5 \]

### Step 5: Solve the Equation
- Rearranging the equation gives:

\[ 45 + 5 = 0.40x \]

\[ 50 = 0.40x \]

- Now, divide both sides by 0.40 to find \( x \):

\[ x = \frac{50}{0.40} \]

- Calculating the right side:

\[ x = 125 \]

### Conclusion
- The shopkeeper sells **125 pencils**.