CAT 2019 Shift 1 Paper

Question : 67 of 100

Marks: +1, -0

Section : QA

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

14π
16π
18π
12π

Validate

Solution:

The distance travelled by bicycle

{B}

in one revolution

=2 π r_{b}=2 π × 40=80 π {cm}

The distance travelled by bicycle

{B}

in one revolution

=2 π r_{b}=2 π × 40=80 π {cm}

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

∴ n × 80 π=(n+5000) × 60 π ⇒ n=15000

Distance travelled by

{B}=n × 80 π {cm}=\;{15000 × 80 π}/{10^{5}} {km}=12 {km}

Time taken by

{B}=45 {min}=\;{45}/{60}=\;{3}/{4} h r {s}

Hence the speed of

{B}=\;{12 π}/{3 {/} 4}=16 π {km} {/} {h}

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