The cost price of 3 exam pads and 2 pencils is Rs. 96.4 exam pads and 3 pencils cost Rs. 134 . Find the total cos t (in Rs.) of an exam pad and that of a pencil

Options

A. 36
B. 38
C. 40
D. 42

Answer

To solve the problem, we need to set up a system of equations based on the information given.

### Step-by-Step Solution:

1. **Define Variables:**
Let the cost of one exam pad be \( x \) (in Rs.) and the cost of one pencil be \( y \) (in Rs.).

2. **Set Up Equations:**
From the problem, we have the following two equations:
- For 3 exam pads and 2 pencils costing Rs. 96:
\[ 3x + 2y = 96 \quad \text{(Equation 1)} \]
- For 4 exam pads and 3 pencils costing Rs. 134:
\[ 4x + 3y = 134 \quad \text{(Equation 2)} \]

3. **Eliminate One Variable:**
To eliminate \( x \), we can multiply Equation 1 by 4 and Equation 2 by 3:
- Multiply Equation 1 by 4:
\[ 12x + 8y = 384 \quad \text{(Equation 3)} \]
- Multiply Equation 2 by 3:
\[ 12x + 9y = 402 \quad \text{(Equation 4)} \]

4. **Subtract the Equations:**
Now, we subtract Equation 3 from Equation 4:
\[ (12x + 9y) - (12x + 8y) = 402 - 384 \]
Simplifying this gives:
\[ y = 18 \]

5. **Substitute Back to Find \( x \):**
Now that we have \( y \), we can substitute it back into Equation 1 to find \( x \):
\[ 3x + 2(18) = 96 \]
Simplifying this:
\[ 3x + 36 = 96 \]
\[ 3x = 96 - 36 \]
\[ 3x = 60 \]
\[ x = 20 \]

6. **Calculate Total Cost:**
Now we find the total cost of one exam pad and one pencil:
\[ x + y = 20 + 18 = 38 \]

### Final Answer:
The total cost of one exam pad and one pencil is Rs. 38.