Latest Others Aptitude Question SOLUTION: Tortoise travels uniformly 20 km a day. The hare, starting from the same point three days later to overtake the tortoise, travels at the uniform rate of 15 km the first day, at a u

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(#M40010557) OTHERS question hare and tortoise Keep an EYE

Tortoise travels uniformly 20 km a day. The hare, starting from the same point three days later to overtake the tortoise, travels at the uniform rate of 15 km the first day, at a uniform rate of 19 km the second day, and so forth in arithmetic progression. After how many days does the hare catches up with the tortoise?

Asked In Others Bankim (11 years ago)

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Garima  (11 years ago)

In 3 days , tortoise has covered 60 kms distance.
In next 2 days, the distance between hare and tortoise has increased to 60+5+1= 66 kms.
From 6 th day, distance is being reduced. First day 3 kms, next day .. 7 kms and so on.
If hare catches tortoise after n+5 days from start of tortoise , then
66 = (n/2)*(2*3+(n-1)*4)

solving it, we get
n=5.5

so hare will catch tortoise on 8th day when it starts running after tortoise.

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teza  (11 years ago)

after 3 days tortoise will cover 60km,
now hare starts its journey(4 day of tortoise)
Arithmetic progression=15,19,23,27,.....(15+4(n-1))
day 1:hare covers 15km tortoise covers :(60+20)=80km
day 2:h:(15+19)=34 t:100
day 3:h:(34+23)=57 t:120
day 4:h:(57+27)=74 t:140
day 5:h:(74+31)=105 t:160
day 6:h:(105+35)=140 t:180
day 7:h:(140+39)=179 t:200
day 8:h:(179+43)=222 t:220
so,hare catches tortoise in 8 days.......

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