How many seconds will a boy take to run one complete round around a square field of side 90 metres, if he runs at a speed of 6 km/hr?

Appeared in: Bihar NHM CHO-2025

Explanation

The total distance covered is the perimeter of the square field, which is calculated as 4 times the side length (4 × 90 m = 360 m).
The speed is given in km/hr and must be converted to meters per second (m/s) to be consistent with the distance unit. The conversion is done by multiplying by 5/18 (6 km/hr × 5/18 = 5/3 m/s).
The time taken is found by dividing the total distance by the speed: Time = Distance / Speed.
Substituting the values: Time = 360 m / (5/3 m/s) = (360 × 3) / 5 = 216 seconds.

Option A: This value is a result of a calculation error. For instance, incorrectly converting the speed or miscalculating the division.
Option B: This value arises from a miscalculation. It does not match the result of dividing the correct distance (360 m) by the correct speed (5/3 m/s).
Option C: This is an incorrect value obtained through calculation errors, possibly in the multiplication or division steps.

Visual 1: Diagram - A square with each side labeled '90 m' and a circular arrow around it to represent 'one complete round'. This helps visualize the path and distance.
Visual 2: Flowchart - A simple flowchart showing the sequence of steps: 1. Calculate Perimeter (4 x 90m) → 2. Convert Speed (6 km/hr to m/s) → 3. Calculate Time (Distance / Speed). This clarifies the logical process.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of time based on speed and distance, involving unit conversion and perimeter of a square as background academic context rather than a clinical decision trigger.
This question tests basic numeracy and problem-solving skills, which are foundational for various calculations in nursing, such as drug dosage, IV drip rates, and intake-output monitoring.
Accuracy in mathematical calculations is critical for patient safety in a clinical setting.
What if the speed was 12 km/hr? The time taken would be halved. Speed = 12 × 5/18 = 10/3 m/s. Time = 360 / (10/3) = 360 × 3 / 10 = 108 seconds. This demonstrates the inverse relationship between speed and time.

How to Approach the Question

First, identify the given information: the shape is a square, the side length is 90 meters, and the speed is 6 km/hr.
Recognize that 'one complete round' means the distance is the perimeter of the square.
Calculate the total distance: Perimeter = 4 × side = 4 × 90 = 360 meters.
Observe that the units for distance (meters) and speed (km/hr) are inconsistent. You must convert one to match the other. Since the answer is required in seconds, convert the speed to m/s.
Use the conversion factor: 1 km/hr = 5/18 m/s. So, 6 km/hr = 6 × (5/18) m/s = 5/3 m/s.
Apply the fundamental formula: Time = Distance / Speed.

Concept Tested & Keywords

Concept Tested: Calculation of time based on speed and distance, involving unit conversion and perimeter of a square.
Stem keywords: square field, side 90 metres, speed of 6 km/hr, one complete round
Lead-in keywords: How many seconds

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Practise the full Bihar NHM CHO-2025

Attempt every question from this paper in a timed mock, then review the full solution for each one.