If a carpenter increases each edge of a square wooden piece from 42 cm to 45 cm, the cost of wood is increased by ₹ 783. What is the rate of wood per sq. cm?

Options

A. ₹3
B. ₹4
C. ₹4.5
D. ₹5

Answer

To solve the problem step-by-step, we will follow these calculations:

### Step 1: Calculate the areas of both squares.
- The area of a square is calculated using the formula:
\[ \text{Area} = \text{side}^2 \]
- For the original square with a side of 42 cm:
\[ \text{Area}_{\text{original}} = 42^2 = 1764 \text{ cm}^2 \]
- For the new square with a side of 45 cm:
\[ \text{Area}_{\text{new}} = 45^2 = 2025 \text{ cm}^2 \]

### Step 2: Find the difference in area.
- The increase in area when the side is increased from 42 cm to 45 cm is:
\[ \text{Increase in Area} = \text{Area}_{\text{new}} - \text{Area}_{\text{original}} = 2025 - 1764 = 261 \text{ cm}^2 \]

### Step 3: Relate the increase in area to the cost.
- We know that the increase in cost due to the increase in area is ₹783. Let the rate of wood per square cm be \( x \).
- The increase in cost can be expressed as:
\[ \text{Increase in Cost} = \text{Increase in Area} \times \text{Rate} = 261x \]
- According to the problem, this increase in cost is equal to ₹783:
\[ 261x = 783 \]

### Step 4: Solve for the rate \( x \).
- To find \( x \), divide both sides of the equation by 261:
\[ x = \frac{783}{261} \]
- Simplifying this:
\[ x = 3 \]

### Conclusion:
- The rate of wood per square cm is ₹3.