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12 May 2021, 03:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
78% (02:59) correct
22%
(03:25)
wrong
based on 265
sessions
History
Date
Time
Result
Not Attempted Yet
Sari and Ken climb up a mountain. At night, they camp together. On the day they are supposed to reach the summit, Sari wakes up at 06:00 and starts climbing at a constant pace. Ken starts climbing only at 08:00, when Sari is already 700 meters ahead of him. Nevertheless, Ken climbs at a constant pace of 500 meters per hour, and reaches the summit before Sari. If Sari is 50 meters behind Ken when he reaches the summit, at what time did Ken reach the summit?
A. 13:00
B. 13:30
C. 14:00
D. 15:00
E. 15:30
A. 13:00
B. 13:30
C. 14:00
D. 15:00
E. 15:30
13 May 2021, 08:48
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Time for which Sari climbs alone = 2 hours.
Distance covered by Sari in these 2 hours = 700 metres (since the question says Sari is 700 metres ahead of Ken)
Therefore, Sari’s speed = 350 metres per hour.
Ken’s speed = 500 metres per hour.
Starting from 8 am till the time Ken reaches the summit, the two persons have climbed for the same time; as such, in this question, the time is constant.
Let us assume that both climbed for ‘t’ hours from 8 am. Then,
Distance covered by Ken to reach the summit = 500t
Distance covered by Sari = 350t.
But, the total distance travelled by Sari is only 50 metres lesser than the total distance travelled by Ken.
Total distance travelled by Ken = 500t (since he only started travelling post 8 am)
Total distance travelled by Sari = 700 + 350t
Therefore, 700 + 350t = 500t – 50. Solving this equation, we get t = 5 hours. 5 hours from 8 am is 1 pm in the afternoon. Therefore, Ken reached the summit at 13:00 hours.
The correct answer option is A.
Hope that helps!
Aravind B T
Distance covered by Sari in these 2 hours = 700 metres (since the question says Sari is 700 metres ahead of Ken)
Therefore, Sari’s speed = 350 metres per hour.
Ken’s speed = 500 metres per hour.
Starting from 8 am till the time Ken reaches the summit, the two persons have climbed for the same time; as such, in this question, the time is constant.
Let us assume that both climbed for ‘t’ hours from 8 am. Then,
Distance covered by Ken to reach the summit = 500t
Distance covered by Sari = 350t.
But, the total distance travelled by Sari is only 50 metres lesser than the total distance travelled by Ken.
Total distance travelled by Ken = 500t (since he only started travelling post 8 am)
Total distance travelled by Sari = 700 + 350t
Therefore, 700 + 350t = 500t – 50. Solving this equation, we get t = 5 hours. 5 hours from 8 am is 1 pm in the afternoon. Therefore, Ken reached the summit at 13:00 hours.
The correct answer option is A.
Hope that helps!
Aravind B T
16 May 2021, 22:37
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Sari's speed= 700/2= 350 m/h
Ken's speed(given)=500m/h
Relative speed= 500-350=150m/h-----> Therefore Ken covers up 150 meters every hour whilst both are traveling
time taken for Ken to cover up 700m from behind(t1=d/s)= 700/150= 14/3hrs----> Therefore they meet at this time.
Now, calculate the time at which the distance between them is 50m.
t2=50/150=1/3hour-----> Therefore after 1/3hour, the distance between them will be 50m.
total time= t1+t2= 14/3+1/3= 15/3= 5hrs.
time at which ken reaches the top= 8:00AM+5hrs= 1:00
Ken's speed(given)=500m/h
Relative speed= 500-350=150m/h-----> Therefore Ken covers up 150 meters every hour whilst both are traveling
time taken for Ken to cover up 700m from behind(t1=d/s)= 700/150= 14/3hrs----> Therefore they meet at this time.
Now, calculate the time at which the distance between them is 50m.
t2=50/150=1/3hour-----> Therefore after 1/3hour, the distance between them will be 50m.
total time= t1+t2= 14/3+1/3= 15/3= 5hrs.
time at which ken reaches the top= 8:00AM+5hrs= 1:00
