Two pens and three pencils cost Rs 86. Four pens and a pencil cost Rs 112. Find the cost of a pen and that of a pencil respectively

Options

A. 12, 25
B. 25, 12
C. 14, 22
D. 22, 14

Answer

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

Let:
- \( P \) = cost of one pen
- \( C \) = cost of one pencil

From the question, we have the following two equations:

1. From the first statement, "Two pens and three pencils cost Rs 86":
\[ 2P + 3C = 86 \quad \text{(Equation 1)} \]

2. From the second statement, "Four pens and one pencil cost Rs 112":
\[ 4P + 1C = 112 \quad \text{(Equation 2)} \]

### Step 1: Multiply Equation 1 to align the coefficients of \( P \)

To eliminate \( P \), we can multiply Equation 1 by 2:
\[ 2(2P + 3C) = 2 \times 86 \]
This gives us:
\[ 4P + 6C = 172 \quad \text{(Equation 3)} \]

### Step 2: Subtract Equation 2 from Equation 3

Now we can subtract Equation 2 from Equation 3:
\[ (4P + 6C) - (4P + 1C) = 172 - 112 \]
This simplifies to:
\[ 5C = 60 \]

### Step 3: Solve for \( C \)

Now, divide both sides by 5 to find the cost of one pencil:
\[ C = \frac{60}{5} = 12 \]

### Step 4: Substitute \( C \) back into one of the original equations to find \( P \)

We can substitute \( C \) back into Equation 1:
\[ 2P + 3(12) = 86 \]
This simplifies to:
\[ 2P + 36 = 86 \]
Now, subtract 36 from both sides:
\[ 2P = 86 - 36 \]
\[ 2P = 50 \]

### Step 5: Solve for \( P \)

Now, divide both sides by 2:
\[ P = \frac{50}{2} = 25 \]

### Conclusion

The cost of a pen is Rs 25 and the cost of a pencil is Rs 12.

### Final Answer:
Cost of a pen = Rs 25, Cost of a pencil = Rs 12.