A man purchased some pens at Rs. 8 each and some pencils at Rs. 2.50 each. If the total number of pens and pencils purchased is 27 and their total cost is Rs. 150, how many pens did he buy?

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define Variables
Let:
- \( x \) = number of pens purchased
- \( y \) = number of pencils purchased

### Step 2: Set Up the Equations
From the problem statement, we have two key pieces of information:
1. The total number of pens and pencils is 27:
\[ x + y = 27 \quad \text{(Equation 1)} \]
2. The total cost of the pens and pencils is Rs. 150:
\[ 8x + 2.5y = 150 \quad \text{(Equation 2)} \]

### Step 3: Eliminate Decimals
To make calculations easier, we can eliminate the decimal in Equation 2 by multiplying the entire equation by 2:
\[ 16x + 5y = 300 \quad \text{(Equation 3)} \]

### Step 4: Solve for One Variable
Now we can solve Equation 1 for \( y \):
\[ y = 27 - x \]

### Step 5: Substitute into the Second Equation
Substitute \( y \) from Equation 1 into Equation 3:
\[ 16x + 5(27 - x) = 300 \]
Expanding this gives:
\[ 16x + 135 - 5x = 300 \]
Combine like terms:
\[ 11x + 135 = 300 \]

### Step 6: Isolate \( x \)
Subtract 135 from both sides:
\[ 11x = 300 - 135 \]
\[ 11x = 165 \]
Now divide by 11:
\[ x = \frac{165}{11} = 15 \]

### Step 7: Find \( y \)
Now that we have \( x \), we can find \( y \):
\[ y = 27 - x = 27 - 15 = 12 \]

### Conclusion
The number of pens purchased is \( x = 15 \).