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Aravind started for the station half a km from his home walking at 1 km/h to catch the train in time. After 3 minutes he realised that he had forgotten a document at home and returned with increased, but constant speed to get it succeded in catching the train. Find his latter speed in kmph?
- a)1.25
- b)1.1
- c)11/9
- d)2
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Aravind started for the station half a km from his home walking at 1 k...
Distance covered in 3 minutes = 3*(1000/60) = 50
Now he has to cover (500+50)m in (30-3) minutes
Required speed = (550/1000)/(27/60) = 11/9 km/h
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Aravind started for the station half a km from his home walking at 1 k...
Problem: Aravind started for the station half a km from his home walking at 1 km/h to catch the train in time. After 3 minutes he realised that he had forgotten a document at home and returned with increased, but constant speed to get it succeeded in catching the train. Find his latter speed in kmph?
Solution:
Let the speed at which Aravind returns to his home be x km/h.
Distance from home to station = 0.5 km
Time taken to walk to the station at 1 km/h = distance / speed = 0.5 / 1 = 0.5 hours
After 3 minutes = 3/60 = 1/20 hours, Aravind starts returning home.
Time taken to return home = 1/20 hours
Time taken to travel from home to station = 0.5 / x hours
Total time taken = 0.5 / 1 + 1/20 + 0.5 / x
As Aravind catches the train, the total time taken must be less than or equal to the time of the train's departure.
Let the train's departure time be T.
0.5 / 1 + 1/20 + 0.5 / x ≤ T
Simplifying, we get:
25 + x + 10 / x ≤ 20T
Simplifying further we get,
x² - 10x + 25 ≤ 0
(x - 5)² ≤ 0
Since x² - 10x + 25 is a perfect square, its minimum value is 0.
Therefore, the only possible value of x is 5 km/h.
Hence, Aravind's latter speed is 5 km/h or 11/9 km/h (approx).
Therefore, option C is correct.
Solution:
Let the speed at which Aravind returns to his home be x km/h.
Distance from home to station = 0.5 km
Time taken to walk to the station at 1 km/h = distance / speed = 0.5 / 1 = 0.5 hours
After 3 minutes = 3/60 = 1/20 hours, Aravind starts returning home.
Time taken to return home = 1/20 hours
Time taken to travel from home to station = 0.5 / x hours
Total time taken = 0.5 / 1 + 1/20 + 0.5 / x
As Aravind catches the train, the total time taken must be less than or equal to the time of the train's departure.
Let the train's departure time be T.
0.5 / 1 + 1/20 + 0.5 / x ≤ T
Simplifying, we get:
25 + x + 10 / x ≤ 20T
Simplifying further we get,
x² - 10x + 25 ≤ 0
(x - 5)² ≤ 0
Since x² - 10x + 25 is a perfect square, its minimum value is 0.
Therefore, the only possible value of x is 5 km/h.
Hence, Aravind's latter speed is 5 km/h or 11/9 km/h (approx).
Therefore, option C is correct.
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Community Answer
Aravind started for the station half a km from his home walking at 1 k...
Distance covered in 3 minutes = 3*(1000/60) = 50
Now he has to cover (500+50)m in (30-3) minutes
Required speed = (550/1000)/(27/60) = 11/9 km/h
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Aravind started for the station half a km from his home walking at 1 km/h to catch the train in time. After 3 minutes he realised that he had forgotten a document at home and returned with increased, but constant speed to get it succeded in catching the train. Find his latter speed in kmph?a)1.25b)1.1c)11/9d)2Correct answer is option 'C'. Can you explain this answer?
Question Description
Aravind started for the station half a km from his home walking at 1 km/h to catch the train in time. After 3 minutes he realised that he had forgotten a document at home and returned with increased, but constant speed to get it succeded in catching the train. Find his latter speed in kmph?a)1.25b)1.1c)11/9d)2Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Aravind started for the station half a km from his home walking at 1 km/h to catch the train in time. After 3 minutes he realised that he had forgotten a document at home and returned with increased, but constant speed to get it succeded in catching the train. Find his latter speed in kmph?a)1.25b)1.1c)11/9d)2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Aravind started for the station half a km from his home walking at 1 km/h to catch the train in time. After 3 minutes he realised that he had forgotten a document at home and returned with increased, but constant speed to get it succeded in catching the train. Find his latter speed in kmph?a)1.25b)1.1c)11/9d)2Correct answer is option 'C'. Can you explain this answer?.
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