Cost of 25 pencils and 20 sharpeners is Rs.100. If the cost of a sharpener is more than the cost of a pencil by 50 paise. What is the total cost of 3 pencils and 4 sharpener

Options

A. Rs. 15
B. Rs. 25
C. Rs. 20
D. None of these

Answer

To solve the problem, we need to find the cost of 3 pencils and 4 sharpeners based on the information provided. Let's break it down step by step.

### Step 1: Define Variables
Let the cost of one pencil be \( x \) rupees. Since the cost of a sharpener is more than the cost of a pencil by 50 paise, we can express the cost of one sharpener as:
\[ \text{Cost of one sharpener} = x + 0.5 \text{ rupees} \]

### Step 2: Set Up the Equation
According to the problem, the total cost of 25 pencils and 20 sharpeners is Rs. 100. We can set up the equation as follows:
\[ 25 \cdot x + 20 \cdot (x + 0.5) = 100 \]

### Step 3: Simplify the Equation
Now, let's simplify the equation:
\[ 25x + 20(x + 0.5) = 100 \]
Expanding the equation:
\[ 25x + 20x + 10 = 100 \]
Combining like terms:
\[ 45x + 10 = 100 \]

### Step 4: Solve for \( x \)
Now, we will isolate \( x \):
\[ 45x = 100 - 10 \]
\[ 45x = 90 \]
\[ x = \frac{90}{45} = 2 \text{ rupees} \]

### Step 5: Find the Cost of a Sharpener
Now that we have the cost of one pencil, we can find the cost of one sharpener:
\[ \text{Cost of one sharpener} = x + 0.5 = 2 + 0.5 = 2.5 \text{ rupees} \]

### Step 6: Calculate the Total Cost of 3 Pencils and 4 Sharpeners
Now, we can find the total cost of 3 pencils and 4 sharpeners:
\[ \text{Total cost} = 3 \cdot x + 4 \cdot (x + 0.5) \]
Substituting the value of \( x \):
\[ = 3 \cdot 2 + 4 \cdot (2 + 0.5) \]
Calculating each part:
\[ = 6 + 4 \cdot 2 + 4 \cdot 0.5 \]
\[ = 6 + 8 + 2 = 16 \text{ rupees} \]

### Final Answer
The total cost of 3 pencils and 4 sharpeners is **Rs. 16**.

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