Question

The wheels of bicycles A and B have radii 30 cm and 40 cm, respectively. While traveling a certain distance, each wheel of A required 5000 more revolutions than each wheel of B. If bicycle B traveled this distance in 45 minutes, then its speed, in km per hour, was

• A. 18π
• B. 16π
• C. 12π
• D. 14π

Answer 1

The Correct Option is B

Bicycle A covers a distance of \(60\pi\) cm per revolution, and bicycle B covers \(80\pi\) cm per revolution. Let B make \(n\) revolutions to cover a certain distance. Then A makes \((n + 5000)\) revolutions to cover the same distance.

Step 1: Equating Distances

Since both bicycles cover the same distance: \[ n \cdot 80\pi = (n + 5000) \cdot 60\pi \]

Step 2: Solving for \(n\)

Divide both sides by \(\pi\): \[ 80n = 60(n + 5000) \] \[ 80n = 60n + 300000 \] \[ 20n = 300000 \Rightarrow n = 15000 \]

Step 3: Distance Travelled

Distance travelled by B: \[ 15000 \cdot 80\pi = 1,200,000\pi \text{ cm} \] Convert to kilometers: \[ \frac{1,200,000\pi}{100000} = 12\pi \text{ km} \]

Step 4: Time and Speed

Time taken = 45 minutes = \(\frac{3}{4}\) hour. 
Speed of B: \[ \frac{12\pi}{3/4} = 16\pi \text{ km/h} \]

Final Answer:

\[ \boxed{16\pi \text{ km/h}} \]