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Time and Distance

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Question
SSCCGLENQA12042620
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A boat takes half time in moving a certain distance downstream than upstream. The ratio of the speed of the boat in still water and that of the current is

  • 2 : 1

  • 1 : 2

  • 4 : 3

  • 3 : 1

Solution

D.

3 : 1

Let the speed of the boat in still water be x kmph. 
Speed of current be y kmph. 
∴  Rate downstream  = (x + y) kmph
   Rate upstream = (x - y) kmph
Distance  = Speed x Time
∴     (x - y) x 2t = (x + y) x t
rightwards double arrow space space 2 straight x space minus space 2 straight y space equals space straight x space plus space straight y rightwards double arrow space space 2 straight x space minus space straight x space space equals space 2 straight y space plus space straight y space rightwards double arrow space space straight x space equals space 3 straight y rightwards double arrow space space space straight x over straight y space equals space space 3 over 1 rightwards double arrow space space space straight x space colon space straight y space equals space 3 space colon space 1

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Question
SSCCGLENQA12042477
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A bus travels 150 Km in 3 hours and then travel next 2 hours at 60 Km/hr. Then the average speed of the bus will be

  • 55 km/hr

  • 54 km/hr

  • 50 km/hr

  • 60 km/hr

Solution

B.

54 km/hr

Total distance covered by the bus  = (150 km + 2 x 60) km
                                                 = (150 + 120) km  = 270 km
∴  Average speed 
               equals space fraction numerator Total space distance over denominator Total space time space taken end fraction equals space 270 over 5 space equals space 54 space kmph.

Question
SSCCGLENQA12043261
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A car can finish a certain journey in 10 hours at the speed of 42 kmph. In order to cover the same distance in 7 hours, the speed of the car (km/h) must be increased by

  • 12

  • 15

  • 18

  • 24

Solution

C.

18

Distance covered by car = Speed x Time = 42 x 10 = 420 km.
New time = 7 hours
therefore space space space Required space speed space equals space 420 over 7 space equals space 60 space kmph
Thus, Required increase in speed = (60 - 42) kmph = 18 kmph

Question
SSCCGLENQA12042869
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A car covers 1 fifth of the distance from A to B at the speed of 8km/hr, 1 over 10 of the distance at 25 km per hour and the remaining at the speed of 20 km per hour. Find the average speed of the whole journey.

  • 12.625 km/hr

  • 13.625 km/hr

  • 14.625 km/hr

  • 15.625 km/hr

Solution

D.

15.625 km/hr

Let the total distance be 1 km.
∴ Total time   open square brackets Time space equals space Distance over Speed close square brackets
equals space fraction numerator 1 over denominator 5 cross times 8 end fraction plus fraction numerator 1 over denominator 10 space cross times space 25 end fraction plus open parentheses fraction numerator 1 minus begin display style 1 fifth end style minus begin display style 1 over 10 end style over denominator 20 end fraction close parentheses equals space 1 over 40 plus 1 over 250 plus open parentheses fraction numerator begin display style fraction numerator 10 minus 2 minus 1 over denominator 10 end fraction end style over denominator 20 end fraction close parentheses equals space 1 over 40 plus 1 over 250 plus 7 over 200 equals fraction numerator 25 plus 4 plus 35 over denominator 1000 end fraction space equals space 64 over 1000 space equals space 8 over 125 space hours
rightwards double arrow space space space space Average space Speed space equals space space space open square brackets fraction numerator Total space distance over denominator Time space taken end fraction close square brackets space equals space 125 over 8 space equals space 15.625 space kmph
   

Question
SSCCGLENQA12043176
Wired Faculty App

A car covers four successive 7km distances at speeds of 10 km/hour, 20 km/hour, 30 km/hour and 60 km/hour respectively. Its average speed over this distance is

  • 30 km/hour

  • 20 km/hour

  • 60 km/hour

  • 40 km/hour

Solution

B.

20 km/hour

Total distance covered = 7 x 4 = 28 km
Total time taken
equals space open parentheses 7 over 10 plus 7 over 20 plus 7 over 30 plus 7 over 60 close parentheses space hours equals space open parentheses fraction numerator 42 plus 21 plus 14 plus 7 over denominator 60 end fraction close parentheses hours equals space 84 over 60 space hours space equals space 7 over 5 space hours
Average Speed
equals space fraction numerator Total space distance space covered over denominator Total space time space taken end fraction space equals space open parentheses fraction numerator 28 over denominator begin display style 7 over 5 end style end fraction close parentheses space kmph equals space fraction numerator 28 space cross times space 5 over denominator 7 end fraction space equals space 20 space kmph

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