Dear Reader,
Below are three easy speed related questions. Some questions would require you to apply simple formulas and some others will require you to apply a bit of logical skills which should be least difficult though.
Question 1
When a lady weighing 48 kg jogged at the rate of 10 km per hour the rate of dissipation of energy was twice that of when she was walking at the rate of 5 km per hour. Similarly the rate of dissipation of energy was higher during summer time than during the winter time. An athlete ran at the rate of 8 km per hour to the victory post and returned at 6 km per hour to the starting point. What is the average speed of the athlete?
a) 5 6/7 km/hr b) 6 6/7 km/hr c) 4 6/7 km/hr d) none of these
Answer : b) 6 6/7 km/hr
Solution :
Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. Then,
the average speed during the whole journey is 2xy / x + y km/hr.
Applying the formula to athlete's case we get his average speed to be
2 x 8 x 6 divided by (8 +6) = 48/7 = 6 6/7 km/hr.
Question 2
A bus was travelling from Koyambedu to Salem Bus Stand via Vellore. A bus was travelling at a speed of 72 km per hour. However when taking into account the stoppage time the average speed became 60 km/hour. How many minutes does the bus stops in an hour?
a) 8 min b) 12 min c) 15 min d) 10 min.
Answer : d)10 min.
Solution :
Due to stoppages, the speed is reduced by 12 km/hr.
In other words, the time that the bus would had taken to drive for 12 Km will be equal to stoppage time per hour.
Time taken to cover 12 km = 12/72 x 60 = 10 min = Stoppage Time.
Question 3
Ram, John and Govind are walking from Marina Beach to Chengalput. Their speeds are in the ratio 4 : 3 : 5. The ratio of the time taken by them to reach Guindy by these persons will be:
a) 15:20:12 b) 4:3:5 c) 15:9:20 d) none of these.
Answer : a) 15:20:12
Solution :
For such problems, one can safely assume distances and speeds but in accordance with the constraints given in the question. For example, if you are going to assume the speeds of Ram, John and Govind, then they should be in the ration 4:3:5. That is their speeds can be 4,3 and 5 Km/hr or 8,6 and 10 Km/hr or 16,12 and 20 Km/hr and so on.
Similarly, the distance from marina to guindy is not given in the question. This means that irrespective of the distance the answer would be same. Hence you can assume any distance from marina to guindy. However, if you assume the distance to be the LCM or multiples of LCM of speeds that is 4,3 and 5, the calculation will become very simple. For example, the LCM of 4,3 and 5 is 60. Hence you can assume the distance to be 60 or 120 or 180.... etc.
In our case, let us assume the speeds to be 4,3 and 5 Km/hr and Distance to be 60 Km.
Ratio of time taken by the three = Distance / Speed of Ram : Distance / Speed of John : Distance / Speed of Govind
= 60/4:60/3:60/5 = 15:20:12
Below are three easy speed related questions. Some questions would require you to apply simple formulas and some others will require you to apply a bit of logical skills which should be least difficult though.
Question 1
When a lady weighing 48 kg jogged at the rate of 10 km per hour the rate of dissipation of energy was twice that of when she was walking at the rate of 5 km per hour. Similarly the rate of dissipation of energy was higher during summer time than during the winter time. An athlete ran at the rate of 8 km per hour to the victory post and returned at 6 km per hour to the starting point. What is the average speed of the athlete?
a) 5 6/7 km/hr b) 6 6/7 km/hr c) 4 6/7 km/hr d) none of these
Answer : b) 6 6/7 km/hr
Solution :
Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. Then,
the average speed during the whole journey is 2xy / x + y km/hr.
Applying the formula to athlete's case we get his average speed to be
2 x 8 x 6 divided by (8 +6) = 48/7 = 6 6/7 km/hr.
Question 2
A bus was travelling from Koyambedu to Salem Bus Stand via Vellore. A bus was travelling at a speed of 72 km per hour. However when taking into account the stoppage time the average speed became 60 km/hour. How many minutes does the bus stops in an hour?
a) 8 min b) 12 min c) 15 min d) 10 min.
Answer : d)10 min.
Solution :
Due to stoppages, the speed is reduced by 12 km/hr.
In other words, the time that the bus would had taken to drive for 12 Km will be equal to stoppage time per hour.
Time taken to cover 12 km = 12/72 x 60 = 10 min = Stoppage Time.
Question 3
Ram, John and Govind are walking from Marina Beach to Chengalput. Their speeds are in the ratio 4 : 3 : 5. The ratio of the time taken by them to reach Guindy by these persons will be:
a) 15:20:12 b) 4:3:5 c) 15:9:20 d) none of these.
Answer : a) 15:20:12
Solution :
For such problems, one can safely assume distances and speeds but in accordance with the constraints given in the question. For example, if you are going to assume the speeds of Ram, John and Govind, then they should be in the ration 4:3:5. That is their speeds can be 4,3 and 5 Km/hr or 8,6 and 10 Km/hr or 16,12 and 20 Km/hr and so on.
Similarly, the distance from marina to guindy is not given in the question. This means that irrespective of the distance the answer would be same. Hence you can assume any distance from marina to guindy. However, if you assume the distance to be the LCM or multiples of LCM of speeds that is 4,3 and 5, the calculation will become very simple. For example, the LCM of 4,3 and 5 is 60. Hence you can assume the distance to be 60 or 120 or 180.... etc.
In our case, let us assume the speeds to be 4,3 and 5 Km/hr and Distance to be 60 Km.
Ratio of time taken by the three = Distance / Speed of Ram : Distance / Speed of John : Distance / Speed of Govind
= 60/4:60/3:60/5 = 15:20:12
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