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Nidhi reached her institute in 3 hours while travelling by bus with a wheel radius of 70 cm and making 250 revolutions in one minute. One day, she left for the institute one hour later than usual time. Then to reach her institute on time, she should increase her speed by ____. [Use π=227\pi = \frac{22}{7}]

Solution

✅ Correct Option: 2

Circumference of the wheel = 2πr=2×227×70=4402\pi r = 2 \times \frac{22}{7} \times 70 = 440 cm.

Number of revolutions per minute = 250.

Distance covered in one minute = Circumference ×\times Revolutions = 440×250=110000440 \times 250 = 110000 cm = 1100 m = 1.1 km.

Speed of the bus = Distance per minute ×\times 60 minutes/hour = 1.1×60=661.1 \times 60 = 66 km/hr.

Usual time taken = 3 hours.

Total distance to the institute = Speed ×\times Time = 66×3=19866 \times 3 = 198 km.

One day, she left 1 hour late, so the available time to reach on time = 3−1=23 - 1 = 2 hours.

Required speed to cover 198 km in 2 hours = 1982=99\frac{198}{2} = 99 km/hr.

Increase in speed required = Required speed - Usual speed = 99−66=3399 - 66 = 33 km/hr.

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