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Narayan Murthy walking at a speed of 20 km/h reaches his college 10 minutes late. Next time he increases his speed by 5 km/h, but finds that he is still late by 4 minutes. What is the distance of his college from his house?
- a)20 km
- b)6 km
- c)12 km
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Narayan Murthy walking at a speed of 20 km/h reaches his college 10 mi...
By increasing his speed by 25%, he will reduce his time by 20%.
(This corresponds to a 6 minute drop in his time for travel—since he goes from being 10 minutes late to only 4 minutes late.)
Hence, his time originally must have been 30 minutes.
Hence, the required distance is 20 kmph × 0.5 hours = 10 km.
(This corresponds to a 6 minute drop in his time for travel—since he goes from being 10 minutes late to only 4 minutes late.)
Hence, his time originally must have been 30 minutes.
Hence, the required distance is 20 kmph × 0.5 hours = 10 km.
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Community Answer
Narayan Murthy walking at a speed of 20 km/h reaches his college 10 mi...
Let's assume the distance between Narayan Murthy's house and his college is 'd' km.
Let's calculate the time taken by Narayan Murthy to reach his college at a speed of 20 km/h.
Speed = Distance/Time
20 = d/Time
Since the speed is given in km/h and the time taken is given in minutes, we need to convert the speed to km/minute.
20 km/h = (20/60) km/minute = 1/3 km/minute
Now, let's calculate the time taken by Narayan Murthy to reach his college at a speed of 1/3 km/minute.
Time = Distance/Speed = d/(1/3) = 3d minutes
It is given that he reaches his college 10 minutes late, so the actual time taken is 3d + 10 minutes.
Next, let's calculate the time taken by Narayan Murthy to reach his college at a speed of 25 km/h.
25 km/h = (25/60) km/minute = 5/12 km/minute
Now, let's calculate the time taken by Narayan Murthy to reach his college at a speed of 5/12 km/minute.
Time = Distance/Speed = d/(5/12) = (12/5)d minutes
It is given that he reaches his college 4 minutes late, so the actual time taken is (12/5)d + 4 minutes.
According to the given information, the actual time taken at a speed of 20 km/h is 3d + 10 minutes, and the actual time taken at a speed of 25 km/h is (12/5)d + 4 minutes.
Since the distances are the same, we can equate the two expressions for time:
3d + 10 = (12/5)d + 4
Simplifying the equation, we get:
15d + 50 = 12d + 20
3d = 30
d = 10
Therefore, the distance of his college from his house is 10 km.
Hence, the correct answer is option D) None of these.
Let's calculate the time taken by Narayan Murthy to reach his college at a speed of 20 km/h.
Speed = Distance/Time
20 = d/Time
Since the speed is given in km/h and the time taken is given in minutes, we need to convert the speed to km/minute.
20 km/h = (20/60) km/minute = 1/3 km/minute
Now, let's calculate the time taken by Narayan Murthy to reach his college at a speed of 1/3 km/minute.
Time = Distance/Speed = d/(1/3) = 3d minutes
It is given that he reaches his college 10 minutes late, so the actual time taken is 3d + 10 minutes.
Next, let's calculate the time taken by Narayan Murthy to reach his college at a speed of 25 km/h.
25 km/h = (25/60) km/minute = 5/12 km/minute
Now, let's calculate the time taken by Narayan Murthy to reach his college at a speed of 5/12 km/minute.
Time = Distance/Speed = d/(5/12) = (12/5)d minutes
It is given that he reaches his college 4 minutes late, so the actual time taken is (12/5)d + 4 minutes.
According to the given information, the actual time taken at a speed of 20 km/h is 3d + 10 minutes, and the actual time taken at a speed of 25 km/h is (12/5)d + 4 minutes.
Since the distances are the same, we can equate the two expressions for time:
3d + 10 = (12/5)d + 4
Simplifying the equation, we get:
15d + 50 = 12d + 20
3d = 30
d = 10
Therefore, the distance of his college from his house is 10 km.
Hence, the correct answer is option D) None of these.
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