A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the hare in the other. The hare starts after the tortoise has covered 1/5 of its distance and that too leisurely. The hare and tortoise meet when the hare has covered only 1/8 of the distance. By what factor should the hare increase its speed so as to tie the race?
Select the correct option.
A) 37.9
B) 37.2
C) 37.1
D) 37.82
E) 37.8
Assume the circumference of the circle is 200 meters. Hare and tortoise started at the same point but moves in the opposite direction. It is given that by that time tortoise covered 40 m (1/5th of the distance), Hare started and both met after hare has covered 25. This implies, in the time hare has covered 25m, hare has covered 200 - 40 - 25= 
<gadget id="calculator">200 - 40 - 25</gadget>
<output>135</output>
135 meters.   So Hare : tortoise speeds= 25 : 135 = 5 : 27   Now Hare and tortoise has to reach the starting point means, Hare has to cover 175 meters and Tortoise has to cover only 25 meters in the same time.   As time =DistanceSpeed=2527=1755×KDistanceSpeed=2527=1755×K   Ie., Hare has to increase its speed by a factor K. Solving we get K = 37.8   Answer:37.8
<result>E</result>
A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the hare in the other. The hare starts after the tortoise has covered 1/5 of its distance and that too leisurely. The hare and tortoise meet when the hare has covered only 1/8 of the distance. By what factor should the hare increase its speed so as to tie the race?