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71. A man can row 15 km/h in still water and he finds that it takes him twice as much time to row up than as to row down the same distance in the river. The speed of current (in km/h) :
15 + x = 30 - 2x
3x = 30 - 15
3x = 15
x = 5 km/h
Solution:
Let the speed of the current be x km/h. Now, according to the question,15 + x = 30 - 2x
3x = 30 - 15
3x = 15
x = 5 km/h
72. A boat covers 48 km upstream and 72 km downstream in 12 hours, while it covers 72 km upstream and 48 km downstream in 13 hours The speed of stream is :
On solving the equation (1) and (2), we get
D = 12 kmph and
U = 8 kmph
Thus, speed of the current
Solution:
Let downstream speed be D and Upstream speed be U. Then On solving the equation (1) and (2), we get
D = 12 kmph and
U = 8 kmph
Thus, speed of the current
73. A motor boat takes 2 hours to travel a distance of 9 km downstream and it takes 6 hours to travel the same distance against the current. The speed of the boat in still water and that of the current (in km/h) respectively are:
= = 4.5 kmph
Upstream speed,
= = 1.5 kmph
Thus, speed of boat in still water,
= = 3 km/h
Speed of current = = 1.5 km/h
Solution:
Downstream speed,= = 4.5 kmph
Upstream speed,
= = 1.5 kmph
Thus, speed of boat in still water,
= = 3 km/h
Speed of current = = 1.5 km/h
74. A train met with an accident 120 km from station A. It completed the remaining journey at of its previous speed and reached 2 hour late at station B. Had the accident taken place 300 km further, it would have been only 1 hour late. What is the speed of the train?
If speed becomes then time taken will be of original time.
Thus, extra time = 2 hour
= 2 hour
Thus unusual time which is require to complete the journey = 5 × 2 = 10 hours.
It means It covers 300 km distance in 5 hours.
then speed = = 60 km/h
Solution:
A ____100 km____ P1 ________300 km_____ P2 ____X______ BIf speed becomes then time taken will be of original time.
Thus, extra time = 2 hour
= 2 hour
Thus unusual time which is require to complete the journey = 5 × 2 = 10 hours.
It means It covers 300 km distance in 5 hours.
then speed = = 60 km/h
75. A runs times as fast as B. If A gives B a start of 300 m, how far must the winning post be if both A and B have to end the race at same time?
Now,
7x - 4x = 300 (A runs 7x m and B runs 4x)
x = 100
7x = 7 × 100 = 700 m
Winning post is 700 m away, As A runs 700 m to complete the race.
Solution:
| . | A | B | Reason (ST=D) |
| Speed | 7 | 4 | Given |
| Time | 4 | 7 | Since, Speed ∝ |
| Distance | 4 | 7 | Distance ∝ time |
Now,
7x - 4x = 300 (A runs 7x m and B runs 4x)
x = 100
7x = 7 × 100 = 700 m
Winning post is 700 m away, As A runs 700 m to complete the race.
76. The wheel of an engine of 300 cm in circumference makes 10 revolutions in 6 seconds. What is the speed of the wheel (in km/h)?
Distance covered in 10 revolutions = 300 * 10 = 3000 cm = 30 m
30 meters are covered in 6 seconds.
Speed of the wheel = = 5 m/s
5 m/s = = 18 km/h. [ To convert m/s to km/h, we use to multiply by factor ]
Solution:
Circumference = One revolutionDistance covered in 10 revolutions = 300 * 10 = 3000 cm = 30 m
30 meters are covered in 6 seconds.
Speed of the wheel = = 5 m/s
5 m/s = = 18 km/h. [ To convert m/s to km/h, we use to multiply by factor ]
77. A thief sees a jeep at a distance of 250 m, coming towards him at 36 km/h. Thief takes 5 seconds to realize that there is nothing but the police is approaching him by the jeep and start running away from police at 54 km/h. But police realise after 10 second, when the thief starts running away, that he is actually a thief and gives chase at 72 km/h. How long after thief saw police did catchup with him and what is the distance police had travel to do so?
Increased speed of the Police = 20 m/s
Speed of the thief = 15 m/s
Initial difference between speed of thief and police = 250 m
After 5 seconds difference between thief and police = 200 + (5 × 10) = 250 m
Now, the time required by police to catch the thief = = 50 s
Total time = 50 + 15 = 65 s
Total distance = 1000 + (15 × 10) = 1150 m.
Solution:
Initial speed of the police = 10 m/sIncreased speed of the Police = 20 m/s
Speed of the thief = 15 m/s
Initial difference between speed of thief and police = 250 m
After 5 seconds difference between thief and police = 200 + (5 × 10) = 250 m
Now, the time required by police to catch the thief = = 50 s
Total time = 50 + 15 = 65 s
Total distance = 1000 + (15 × 10) = 1150 m.
78. A person X starts from Lucknow and another person Y starts from Kanpur to meet each other. Speed of X is 25 km/h, while Y is 35 km/h. If the distance between Lucknow and Kanpur be 120 km and both X and Y start their journey at the same time, when they will meet ?
Relative speed = (25+35) = 60 km/h
Time taken to complete 120 km,
= = 2 h
Thus, They will meet 2 hours later.
Solution:
Lucknow(X →)_____120 km _____(← Y)KanpurRelative speed = (25+35) = 60 km/h
Time taken to complete 120 km,
= = 2 h
Thus, They will meet 2 hours later.
79. Two persons A and B started from two different places towards each other. If the ratio of their speed be 3 : 5, then what is the ratio of distance covered by A and B respectively till the point of meeting?
Solution:
When time is constant the distance covered by A and B will be in the ratio of their speeds.i.e. ratio of distance is 3 : 5 as time is constant.
80. The ratio of speeds of A and B is 2 : 3 and therefore A takes 20 minutes more time than B. What is the ratio of time taken by A and B?
ST = D
When distance constant,
S ∝
So, ratio of time taken by A and B = 3 : 2
Solution:
When distance is constant then Speed is inversely proportional to time.ST = D
When distance constant,
S ∝
So, ratio of time taken by A and B = 3 : 2