Cost of 4 pens, 6 note books and 9 files is Rs 305. Cost of 3 pens, 4 notebooks and 2 files is Rs 145. What is the cost (in Rs) of 5 pens, 8 notebooks and 16 files?

Options

A. 415
B. 465
C. 440
D. Cannot be determined

Answer

To solve the problem step by step, we can set up equations based on the information given.

### Step 1: Define Variables
Let:
- \( P \) = cost of one pen
- \( N \) = cost of one notebook
- \( F \) = cost of one file

### Step 2: Set Up Equations
From the problem statement, we can create the following equations based on the costs provided:

1. For the first condition (cost of 4 pens, 6 notebooks, and 9 files):
\[ 4P + 6N + 9F = 305 \quad \text{(Equation 1)} \]

2. For the second condition (cost of 3 pens, 4 notebooks, and 2 files):
\[ 3P + 4N + 2F = 145 \quad \text{(Equation 2)} \]

### Step 3: Subtract the Equations
Now, we will subtract Equation 2 from Equation 1 to eliminate some variables:

\[ (4P + 6N + 9F) - (3P + 4N + 2F) = 305 - 145 \]

This simplifies to:

\[ (4P - 3P) + (6N - 4N) + (9F - 2F) = 160 \]

Which gives us:

\[ P + 2N + 7F = 160 \quad \text{(Equation 3)} \]

### Step 4: Add Equations
Next, we will add Equation 1 and Equation 3:

\[ (4P + 6N + 9F) + (P + 2N + 7F) = 305 + 160 \]

This simplifies to:

\[ (4P + P) + (6N + 2N) + (9F + 7F) = 465 \]

Which gives us:

\[ 5P + 8N + 16F = 465 \quad \text{(Equation 4)} \]

### Step 5: Conclusion
The final equation (Equation 4) directly gives us the cost of 5 pens, 8 notebooks, and 16 files:

\[ 5P + 8N + 16F = 465 \]

Thus, the cost of 5 pens, 8 notebooks, and 16 files is **Rs. 465**.