Bicycle Wheel Revolutions and Speed

CAT 2019 Slot 1 · QA · Medium · Speed, time & distance

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The wheels of bicycles A and B have radii 30 cm30\text{ cm} and 40 cm40\text{ 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

  1. A.

    18\pi

  2. B.

    16\pi

  3. C.

    12\pi

  4. D.

    14\pi

Answer

B

Explanation

Circumference of wheel A =2π(30)=60π cm=0.6π m= 2\pi(30) = 60\pi\text{ cm} = 0.6\pi\text{ m}. Circumference of wheel B =2π(40)=80π cm=0.8π m= 2\pi(40) = 80\pi\text{ cm} = 0.8\pi\text{ m}. Let distance be D metersD\text{ meters}. D0.6π−D0.8π=5000  ⟹  Dπ(106−108)=5000  ⟹  Dπ(512)=5000  ⟹  D=12000π meters=12π km\frac{D}{0.6\pi} - \frac{D}{0.8\pi} = 5000 \implies \frac{D}{\pi}\left(\frac{10}{6} - \frac{10}{8}\right) = 5000 \implies \frac{D}{\pi}\left(\frac{5}{12}\right) = 5000 \implies D = 12000\pi\text{ meters} = 12\pi\text{ km}. Time for B =45 minutes=3/4 hour= 45\text{ minutes} = 3/4\text{ hour}. Speed of B =12π3/4=16π km/h= \frac{12\pi}{3/4} = 16\pi\text{ km/h}.

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