Question

A farmer cultivates his land with a country plough of size 15 cm. How many km the farmer has to walk for ploughing one ha of land

• A. 30.3
• B. 45.6
• C. 66.7
• D. 60.5

Hint:

To find the distance walked in kilometers per hectare quickly, use this simple shortcut formula:
\[ \text{Distance (km/ha)} = \frac{10}{\text{Width of Implement (m)}} \] Here, $\frac{10}{0.15} = 66.67\text{ km}$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The distance walked by a farmer during field operations depends on the effective working width of the implement and the total area of the field.
By treating the ploughed path as a continuous series of parallel strips, the total path length is equal to the field area divided by the implement width.
Key Formula or Approach:
The total distance walked ($D$, in meters) is calculated using the relation:
\[ D = \frac{\text{Area } (A)}{\text{Width of Implement } (W)} \] where:
$A = 1\text{ ha} = 10,000\text{ m}^2$
$W = 15\text{ cm} = 0.15\text{ m}$

Step 2: Detailed Explanation:
Let us substitute the given values into the formula to find the distance in meters:
\[ D = \frac{10,000 \text{ m}^2}{0.15 \text{ m}} \] \[ D \approx 66,666.67 \text{ meters} \] Now, we convert the distance from meters to kilometers:
\[ D_{\text{km}} = \frac{66,666.67 \text{ m}}{1000} \approx 66.67 \text{ km} \] This calculation assumes no overlap between adjacent runs and ignores the turning distances at the headlands, representing the minimum theoretical distance the farmer must walk.

Step 3: Final Answer:
The farmer has to walk approximately $66.7\text{ km}$ to plough one hectare of land using a $15\text{ cm}$ plough.