CAT 2019 Slot 1 QA Question & Solution

ArithmeticMedium

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

Options

$18 \pi$

$14 \pi$

$16 \pi$

$12 \pi$

Solution

Distance covered by A in 1 revolution = $2\pi \times 30 = 60\pi$

Distance covered by B in 1 revolution = $2\pi \times 40 = 80\pi$

Now, $(5000+n)60\pi = 80\pi n$

$\Rightarrow 15000 = 4n-3n \Rightarrow n = 15000$

Then distance travelled by B = $15000 \times 80\pi \text{ cm} = 12\pi \text{ km}$

Hence, the speed = $\frac{12\pi \times 60}{45} = 16\pi$