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81. Two trains starting at the same time from two-stations 300 km apart and going in opposite directions, cross each other at a distance of 160 km from one of them. The ratio of their speeds is :
Ratio of their distance covered = = 8 : 7
Then,
Ratio of their speeds = 8 : 7 [When time is constant Speed is proportional to Distance covered]
Solution:
A → ___160________Meeting____140_____← BRatio of their distance covered = = 8 : 7
Then,
Ratio of their speeds = 8 : 7 [When time is constant Speed is proportional to Distance covered]
82. Two runner start running together for a certain distance, one at 5 km/h and another at 8 km/h. The former arrives one and half an hour before the latter. The distance in Km is :
Solution:
83. A railway passenger counts the telegraph poles on the rail road as he passes them. The telegraph poles are at a distance of 50 metres. What will be his count in 4 hours, if the speed of the train is 45 km per hour.
Thus, the no. of poles,
= = 3600 [Poles are at the distance of 50 m.]
Solution:
In train he travels = 4 × 45 = 180 km = 180000 mThus, the no. of poles,
= = 3600 [Poles are at the distance of 50 m.]
84. Without stoppage, a train travels a certain distance with an average speed of 60 km/h, and with stoppage it covers the same distance with an average speed of 40 km/h. On an average, how many minutes per hour does train stop during the journey ?
Hence,
If it's speed with stoppage is 40 km/h, it will travel 40 minutes per hour i.e. train stops 20 min/hour.
Solution:
Since, the train travels at 60 km/h, it's speed per minute is 1 km per minute.Hence,
If it's speed with stoppage is 40 km/h, it will travel 40 minutes per hour i.e. train stops 20 min/hour.
85. A train without stopping travels 60 km/h and with stoppage 40 km/h. What is the time taken for stoppage on a route 300 km?
Time taken to travel 300 km with stoppage,
Time taken for stoppage as it stops for 20 min per hour
= 7 × 20 + 10
= 140 + 10
= 150 minutes.
= hours = 2.5 hours.
Solution:
Since, the train travels at 60 km/h, it's speed per minute is 1 km per minute. Hence, if it's speed with stoppage is 40 km/h, it will travel 40 minutes per hour i.e. train stops 20 min per hour.Time taken to travel 300 km with stoppage,
Time taken for stoppage as it stops for 20 min per hour
= 7 × 20 + 10
= 140 + 10
= 150 minutes.
= hours = 2.5 hours.
86. Narayan 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?
Hence, his time originally must have been 30 minutes.
Thus required distance = 20 kmph × 0.5 hours = 10 km.
Solution:
By increasing his speed by 25%, he will reduce his time by 20%. (This corresponds to a 6 minutes drop in his time.)Hence, his time originally must have been 30 minutes.
Thus required distance = 20 kmph × 0.5 hours = 10 km.
87. A motor car does a journey in 17.5 hours, covering the first half at 30 km/h and the second half at 40 km/h. Find the distance of the journey?
A_____X km_____M_____X km_____B
Total time taken in the journey = 17.5 hours
Time taken to cover X km at 30 km/h =
Time taken to cover X km at 40 km/h =
Now,
Solution:
Let the total distance be 2X.A_____X km_____M_____X km_____B
Total time taken in the journey = 17.5 hours
Time taken to cover X km at 30 km/h =
Time taken to cover X km at 40 km/h =
Now,
88. A car after traveling 18 km from a point A developed some problem in the engine and the speed became th of its original speed. As a result, the car reached point B 45 minutes late. If the engine had developed the same problem after traveling 30 km from A, then it would have reached 36 minutes late. The original speed of the car (in km/h) is:
Now the main difference comes in those 12km (30 - 18) and the change in difference of time = (45 - 36) min = 9 min
Thus,
× T = 9 min where T is the time required to cover the distance of (30 - 18) = 12 km
T = 36 min = hours = 0.6 hours.
Speed of the car = = 20 kmph.
Solution:
He proceeds at S where S is his usual speed means decrease in speed which will lead to increase in time.Now the main difference comes in those 12km (30 - 18) and the change in difference of time = (45 - 36) min = 9 min
Thus,
× T = 9 min where T is the time required to cover the distance of (30 - 18) = 12 km
T = 36 min = hours = 0.6 hours.
Speed of the car = = 20 kmph.
89. A hunter fired two shots from the branch of a tree at an interval of 76 seconds. A tiger separating too fast hears the two shots at an interval of 83 seconds. If the velocity of the sound is 1195.2 km/h, then find the speed of the tiger.
S = 100.8 km/h.
Solution:
In the case of increasing gap between two objects, we haveS = 100.8 km/h.
90. A man can cross a downstream river by steamer in 40 minutes and same by boat in 1 hour. If the time of crossing Upstream by streamer is 50% more than downstream time by steamer and the time required by boat to cross same river by boat in upstream is 50% more than time required by in downstream. What is the time taken for the man to cross the river downstream by steamer and then return to same place by boat half the way and by steamer the rest of the way?
Downstream (boat) = 60 min
Upstream (steamer) = 60 min
Upstream (boat) = 90 min
Required time = 40 + 30 + 45 = 115 minutes
Solution:
Downstream (steamer) = 40 minDownstream (boat) = 60 min
Upstream (steamer) = 60 min
Upstream (boat) = 90 min
Required time = 40 + 30 + 45 = 115 minutes