The speed of the cycle changes with the change in speed of wind. Time taken by cycle to travel 20 km., is 2 hours when wind is in the direction of the cycle moving, and time taken to travel the same distance against the wind is 3 hours. Find out the percentage increase in speed of the cycle to cover the distance in same time.
Let the speed of cycle be ‘X’ km/hr. and speed of wind be ‘Y’ km/hr. As per the question, X+Y = 20/2 X+Y = 10 km/hr.-------------- (1) X-Y = 20/3 Km/hr.------------(2) Solving (1) and (2) X= 50/6 Km/hr. Y = 10/6 Km/hr. Speed is required to cover the 20 km in 2 hr. When the speed of wind is against the cycle. 10= S-(10/6) S= 10+(10/6) S= 70/6 Km/hr. Required Increased in Speed = 70/6-50/6 = 20/6 Required percentage = (20/6)/ (50/6) x 100 = 40%
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