Step 1: Understanding the Question:
The provided question text is incomplete and missing the specific traveling speeds due to an OCR error ("He travelled partly on foot is").
However, based on standard variations of this classic math problem, the full text typically states: "He travelled partly on foot at 4 km/hr and partly on bicycle at 9 km/hr. Find the distance travelled on foot."
We will proceed using these standard values to demonstrate the full solution, which perfectly aligns with the given options.
A farmer covers a total distance of 61 km over a total time of exactly 9 hours using two different modes of transport.
Step 2: Key Formula or Approach:
We will use the fundamental distance formula: $\text{Distance} = \text{Speed} \times \text{Time}$.
Let the time the farmer spent walking on foot be $t$ hours.
Consequently, the time spent riding the bicycle will be $(9 - t)$ hours.
We will set up a linear equation adding the distances covered by each mode of transport and equate it to the total 61 km.
Step 3: Detailed Explanation:
We assume the standard speeds: Speed on foot = 4 km/hr, Speed on bicycle = 9 km/hr.
Let the time traveled on foot be $t$ hours.
Since the total travel time is 9 hours, the time traveled on the bicycle is $(9 - t)$ hours.
The distance traveled on foot is $\text{Speed} \times \text{Time} = 4 \times t = 4t$ km.
The distance traveled on the bicycle is $\text{Speed} \times \text{Time} = 9 \times (9 - t)$ km.
According to the problem, the total distance covered is 61 km.
Therefore, we can write the equation: $4t + 9(9 - t) = 61$.
We expand the terms inside the parentheses: $4t + 81 - 9t = 61$.
Combining the $t$ terms gives: $81 - 5t = 61$.
We rearrange the equation to isolate $5t$: $5t = 81 - 61$.
$5t = 20$.
Dividing both sides by 5 gives the time spent walking: $t = 4$ hours.
The question asks for the total distance travelled on foot.
Distance on foot = $4t = 4 \times 4 = 16$ km.
This perfectly matches the first option.
Step 4: Final Answer:
The distance travelled on foot is 16 km.