The diameter of the wheel of a bicycle is 21 cm. A cyclist travels at a speed of 16.5 km/h and takes 45 minutes to reach a destination. How many complete revolutions does the wheel make during the journey?

Introduction / Context:
This is a classic speed, distance and mensuration question often seen in aptitude exams. The idea is that the distance travelled by a bicycle equals the number of wheel revolutions multiplied by the circumference of the wheel. We are given the speed, the travel time and the wheel diameter, and we must compute the number of revolutions. The solution involves unit conversion between kilometres and centimetres and the correct use of the circle circumference formula.

Given Data / Assumptions:
- Wheel diameter D = 21 cm. - Wheel radius r = D / 2 = 10.5 cm. - Cyclist speed v = 16.5 km per hour. - Travel time t = 45 minutes. - Use π = 22 / 7 for circumference if needed. - Distance travelled = speed * time with consistent units.

Concept / Approach:
The distance travelled by the bicycle in a straight line equals the total length of all the circular paths traced by a point on the tyre. Each revolution covers one circumference of the wheel. Therefore, Number of revolutions = Total distance travelled / Circumference of the wheel. To keep calculations simple, convert the total distance to centimetres so that it matches the circumference units, and then divide. This avoids mixing units of kilometres, metres and centimetres within one formula.

Step-by-Step Solution:
Step 1: Convert time to hours: 45 minutes = 45 / 60 = 0.75 hours. Step 2: Compute distance in kilometres: distance = speed * time = 16.5 * 0.75. Step 3: Multiply 16.5 by 0.75 to get 12.375 km. Step 4: Convert distance to metres: 12.375 km = 12.375 * 1000 = 12375 metres. Step 5: Convert distance to centimetres: 12375 metres = 12375 * 100 = 1237500 cm. Step 6: Compute wheel circumference: C = π * D = (22 / 7) * 21. Step 7: Evaluate C = (22 / 7) * 21 = 22 * 3 = 66 cm. Step 8: Number of revolutions = total distance / circumference = 1237500 / 66. Step 9: Compute 1237500 / 66 = 18750.

Verification / Alternative check:
We can check the plausibility by approximating. If the circumference is about 0.66 metres (since 66 cm = 0.66 m) and the total distance is 12375 metres, then the number of revolutions is roughly 12375 / 0.66. This also gives around 18750, which supports the exact calculation. Additionally, we can check that the units are consistent: dividing centimetres by centimetres produces a dimensionless count, which is correct for a number of revolutions.

Why Other Options Are Wrong:
Option 12325 does not correspond to any simple miscalculation step and is far from the value produced by the distance to circumference ratio. Option 21000 would be obtained if one mistakenly used an incorrect circumference or distance conversion, overestimating the number of revolutions. Option 24350 is much larger than the correct value and would imply either a much longer journey or a much smaller wheel than stated.

Common Pitfalls:
Typical mistakes include forgetting to convert time into hours, converting kilometres directly to centimetres incorrectly, or using radius instead of diameter in the circumference formula as π * r instead of 2 * π * r or π * D. Some learners also mix metres and centimetres in the same computation, which leads to wrong ratios. Keeping track of units at each step and explicitly converting everything into centimetres is a reliable way to avoid such errors.

Final Answer:
The wheel makes 18750 complete revolutions during the journey.