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200 m race

by harsh.champ » Fri Feb 19, 2010 10:36 am
In a 200m race, if Tom gives Harry a start of 25 metres, then Tom wins the race by 10 seconds. Alternatively, if Tom gives Harry a start of 45 metres the race ends in a dead heat. How long does Tom take to run 200m?


A. 77.5 seconds
B. 87.5 seconds
C. 90 seconds
D. 100 seconds
E. 112.5 seconds

The OA is A.
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by ajith » Fri Feb 19, 2010 12:16 pm
harsh.champ wrote:In a 200m race, if Tom gives Harry a start of 25 metres, then Tom wins the race by 10 seconds. Alternatively, if Tom gives Harry a start of 45 metres the race ends in a dead heat. How long does Tom take to run 200m?


A. 77.5 seconds
B. 87.5 seconds
C. 90 seconds
D. 100 seconds
E. 112.5 seconds

The OA is A.
Say Harry is running x meters per second and Tom is running at y meters per second

45 +x*t = y*t
25 + x*(t+10) = y*t

25 + x*(t+10) =45 +x*t
25+ x*t +10x = 45 +x*t
10x = 20
x=2

45 + 2*t = 200
t =155/2 = 77.5
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by harsh.champ » Fri Feb 19, 2010 12:48 pm
The question can also be answered in this way:-
Tom gives Harry a start of 25 metres and still wins the race by 10 seconds.

Alternatively, if Tom gives Harry a start of 45 metres, then the race ends in a dead heat.

Therefore, the additional 20 metres start given to Harry compensates for the 10 seconds.
i.e., Harry runs 20 metres in 10 seconds.

Hence, Harry will take 100 seconds to run 200 metres.

We know that Tom gives Harry a start of 45 metres. Harry will take 22.5 seconds to run this 45 metres as Harry runs 20 metres in 10 seconds or at the speed of 2 m/s.

Hence,Tom will take 22.5 seconds lesser than Harry or 100 - 22.5 = 77.5 seconds to complete the race.
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by shashank.ism » Sat Feb 20, 2010 7:46 am
harsh.champ wrote:In a 200m race, if Tom gives Harry a start of 25 metres, then Tom wins the race by 10 seconds. Alternatively, if Tom gives Harry a start of 45 metres the race ends in a dead heat. How long does Tom take to run 200m?


A. 77.5 seconds
B. 87.5 seconds
C. 90 seconds
D. 100 seconds
E. 112.5 seconds

The OA is A.
Let speed of tom and harry be u & v respectively and t be the time taken by tom
so 1st case: ut = 25 + vt + 10v -----(i)

2nd case: ut = 45 + vt -----(ii)
I take both time as t only since in both the cases tom runs with same speed and hence to cover full distance he will take t time

from (i) - (ii) , we get
10v - 20 = 0 --> v=2
from (ii) , ut = 45 +2t --> also ut = total distance = 200
--> 200 = 45 +2t --> t = (200-45)/2 = 77.5 Ans A
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