Practice Test on Speed,Time and Distance

1)A train covers a distance in 50 min ,if it runs at a speed
of 48kmph on an average.The speed at which the train must run
to reduce the time of journey to 40min will be.

1. Solution::
   Time=50/60 hr=5/6hr
   Speed=48mph
   distance=S*T=48*5/6=40km
   time=40/60hr=2/3hr
   New speed = 40* 3/2 kmph= 60kmph

 

2)Vikas can cover a distance in 1hr 24min by covering 2/3 of
the distance at 4 kmph and the rest at 5kmph.the total
distance is?

2. Solution::
   Let total distance be S
   total time=1hr24min
   A to T :: speed=4kmph
   diistance=2/3S
   T to S :: speed=5km
   distance=1-2/3S=1/3S
   21/15 hr=2/3 S/4 + 1/3s /5
   84=14/3S*3
   S=84*3/14*3
   = 6km

 

3)walking at ¾ of his usual speed ,a man is late by 2 ½ hr.
the usual time is.

3. Solution::
   Usual speed = S
   Usual time = T
   Distance = D
   New Speed is ¾ S
   New time is 4/3 T
   4/3 T – T = 5/2
   T=15/2 = 7 ½

 

 

4)A man covers a distance on scooter .had he moved 3kmph
faster he would have taken 40 min less. If he had moved
2kmph slower he would have taken 40min more.the distance is.

 

 4.Solution::
Let distance = x m
Usual rate = y kmph
x/y – x/y+3 = 40/60 hr
2y(y+3) = 9x ————–1
x/y-2 – x/y = 40/60 hr y(y-2) = 3x —————–2

divide 1 & 2 equations
by solving we get x = 40

 

5)Excluding stoppages,the speed of the bus is 54kmph and
including stoppages,it is 45kmph.for how many min does the bus
stop per hr.

5.Solution::
Due to stoppages,it covers 9km less.
Time taken to cover 9 km is [9/54 *60] min = 10min

 

6)Two boys starting from the same place walk at a rate of
5kmph and 5.5kmph respectively.wht time will they take to be
8.5km apart, if they walk in the same direction

6.Solution::
The relative speed of the boys = 5.5kmph – 5kmph = 0.5 kmph
Distance between them is 8.5 km
Time= 8.5km / 0.5 kmph = 17 hrs

7)2 trains starting at the same time from 2 stations 200km
apart and going in opposite direction cross each other ata
distance of 110km from one of the stations.what is the ratio of
their speeds.

 

7. Solution::
   In same time ,they cover 110km & 90 km respectively
   so ratio of their speed =110:90 = 11:9

 

8)Two trains start from A & B and travel towards each other at
speed of 50kmph and 60kmph resp. At the time of the meeting the
second train has traveled 120km more than the first.the distance
between them.
8. Solution::
Let the distance traveled by the first train be x km
then distance covered by the second train is x + 120km
x/50 = x+120 / 60
x= 600
so the distance between A & B is x + x + 120 = 1320 km

9)A thief steals a ca r at 2.30pm and drives it at 60kmph.the
theft is discovered at 3pm and the owner sets off in another car
at 75kmph when will he overtake the thief

9. Solution::
   Let the thief is overtaken x hrs after 2.30pm
   distance covered by the thief in x hrs = distance covered by
   the owner in x-1/2 hr
   60x = 75 ( x- ½)
   x= 5/2 hr
   thief is overtaken at 2.30 pm + 2 ½ hr = 5 pm

 

10)In covering distance,the speed of A & B are in the ratio
of 3:4.A takes 30min more than B to reach the destion.The time
taken by A to reach the destinstion is.

10. Solution::
    Ratio of speed = 3:4
    Ratio of time = 4:3
    let A takes 4x hrs,B takes 3x hrs
    then 4x-3x = 30/60 hr
    x = ½ hr
    Time taken by A to reach the destination is 4x = 4 * ½ = 2 hr

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