If the price of 3 pens, 2pencils and 4 erasers is Rs 92 and the price of 8 pencils and 16 erasers is Rs 68, then the price of 24 pens is

Options

A. Rs 675
B. Rs 625
C. Rs 500
D. Rs 600

Answer

To solve the problem, we will set up a system of equations based on the information given and then solve for the price of the pens.

### Step 1: Define Variables
Let:
- \( x \) = price of one pen
- \( y \) = price of one pencil
- \( z \) = price of one eraser

### Step 2: Set Up the Equations
From the problem, we have two equations based on the prices given:
1. From the first statement:
\[ 3x + 2y + 4z = 92 \quad \text{(Equation 1)} \]
2. From the second statement:
\[ 8y + 16z = 68 \quad \text{(Equation 2)} \]

### Step 3: Simplify Equation 2
We can simplify Equation 2 by dividing all terms by 4:
\[ 2y + 4z = 17 \quad \text{(Equation 3)} \]

### Step 4: Substitute Equation 3 into Equation 1
Now, we can express \( 4z \) from Equation 3:
\[ 4z = 17 - 2y \]
Substituting this into Equation 1 gives:
\[ 3x + 2y + (17 - 2y) = 92 \]
This simplifies to:
\[ 3x + 17 - 2y + 2y = 92 \]
\[ 3x + 17 = 92 \]

### Step 5: Solve for \( x \)
Now, isolate \( x \):
\[ 3x = 92 - 17 \]
\[ 3x = 75 \]
\[ x = \frac{75}{3} = 25 \]

### Step 6: Find the Price of 24 Pens
Now that we have the price of one pen, we can find the price of 24 pens:
\[ \text{Price of 24 pens} = 24x = 24 \times 25 = 600 \]

### Final Answer
The price of 24 pens is Rs. 600.

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