CAT 2019 Quant Question with Solution 19

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

  1. $18 \pi$
  2. $12 \pi$
  3. $16 \pi$
  4. $14 \pi$
Show Answer

Correct Answer: Option: 3

The distance travelled by bicycle A in one revolution = $2\pi {{r}_{a}}=2\pi \times 30=60\pi \ cm$

The distance travelled by bicycle B in one revolution = $2\pi {{r}_{b}}=2\pi \times 40=80\pi \ cm$

Let B makes ‘n’ revolutions to cover the distance. Then, A would make (n+5000) to cover the same distance.

$\therefore n\times 80\pi =(n+5000)\times 60\pi $ $\Rightarrow n=15000$

Distance travelled by B = $n\times 80\pi \ cm=\frac{15000\times 80\pi }{{{10}^{5}}}\ km=12\ km$

Time taken by B= 45 min = $\frac{45}{60}=\frac{3}{4}hrs$

Hence the speed of B = $\frac{12\pi }{3/4}=16\pi \ km/h$


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