Friday, 19 February 2016

Aptitude Questions with Answers - Time and Distance Solved Problems 1

Time and Distance Solved Questions


1.    Ravi covers a distance of 900 meters in 180 seconds. Find his speed in kmph?
a)18 kmph      b)12 kmph    c)25 kmph   d)22 kmph
Answer : A
Explanation : Given distance D= 900 meters and Time= 180 seconds
                         Speed =
Distance / Time
=
900 / 180
= 5 m/s.
              But speed is asked in kmph , to convert 5 mps to kmph , multiply it by
18 / 5
.
                  Speed in kmph = 5 x
18 / 5
= 18 kmph

2.    The speed of a vehicle is 54 km/h. What distance it can cover in 18 seconds?
a)100m           b)200m              c)270m                 d)150m
Answer :  C
Explanation : Given speed is in kmph but time is in seconds. So we need to convert speed which is in kmph into mps.
                     54 km/h = 54 x
5 / 18
= 15 m/s.
               Distance it can cover in 18 seconds => Distance = Speed x Time
                    = 15 x 18 = 270 meters

3.    A motor bike can cover a distance of 270 km in 5 hours. What is its speed in m/s ?
a)  12.5 kmph               b)13.3 kmph            c)15 kmph               d)20 kmph
Answer : C
Explanation :  Distance is 270 km and time is 5 hours.
                      Speed =
Distance / Speed
=
270 / 5
= 54 kmph
     But in the given question, speed in m/s is asked.
   Converting obtained speed 54 kmph into m/s = 54 x
5 / 18
= 15 kmph

4.    A car travels at a speed of 30 kmph . How much distance it can cover in 1 hour 40 minutes?
        a)    50 km                     b)60 km                  c)70 km                            d)75 km
Answer : A
Explanation : Time = 1 hour 40 minutes = 1
40 / 60
hours =
5 / 3
hours
               Distance covered by the car = Speed x  Time
                                                        = 30 X
5 / 3
= 50 km

5.    The speed of a car is 60 kmph. A boy runs at one fourth the speed of car and reaches his school from his house in 20 minutes. What is the distance between school and house?            a)    3 km                      b)4 km                             c)5km                     d)6km
Answer : C
Explanation:   Speed of car = 60 kmph.
Boy runs at one fourth the speed of car è Speed of boy = ¼ x 60 kmph = 15 kmph
           Time taken by boy to reach his school = 20 minutes =
1 / 3
rd hour
Distance between his school and house = Speed x Time
                                 =15 x
1 / 3
= 5 km

6.    Raju goes to his office from his house with the speed of 6 kmph and returns with the speed of 8 kmph on his bicycle. What is his average speed of whole journey?
  a)    6.8 kmph     b)7.5 kmph      c)5.5 kmph       d)8 kmph
Answer: A
Explanation: If a person covers two equal distances with the speed of x and y units respectively, then the average speed of the man  for complete journey =
2xy / x+y
             Here x= 6 and y= 8
Average Speed =
2 x 6 x 8 / 6+8
= 6.8 kmph approximately

7.    A car covers first half distance with the speed of 50 kmph and second half distance with speed of 40 kmph. It takes 9 hours to cover total distance. What is the distance covered in whole journey?  
  a)    250 km     b)330 km       c)350 km      d)400 km
Answer : D
Explanation: It covered the total distance in two equal parts with speeds of 50 and 40 kmph.
Average speed of the journey =
2xy / x+y
   =
2 x 50 x 40 / 50+40
=
400 / 9
It takes 9 hours to cover the total distance
     Distance covered = Average speed x Time
              =
400 / 9
   x 9 = 400 km

8.    A car covers 100 km at a speed of 20 kmph and then further travels 210 km at a speed of 70 kmph .What is the average speed of the car?
a)35 kmph      b)38.75 kmph        c)45 kmph         d)60 kmph
Answer :B
Explanation :
Time taken to cover 100km =
Distance / Speed
=
100 / 20
= 5 hours
Time taken by car to cover next 210 km =
Distance / Speed
=
210 / 70
= 3 hours
   Total distance covered = 100 km + 210 km = 310 km
     Total time taken = 5 hours  + 3 hours = 8 hours
    Therefore, average speed =
Total Distance / Total Time
 =
310 / 8
hours = 38.75 kmph

9.    Car A takes 40 minutes to cover a distance of 120km. If the speed of Car B  25% faster than Car A , it will cover the same distance in
a)24 min   b)32 min        c)38 min       d)40 min
Answer: B
Explanation:
Speed of car B is 25% faster than Car A => Car B =
125 / 100
Car A
  The ratio of speeds of car A and car B = 100 : 125 =4 :5
The Ratio of times taken by car A and B to cover same distance = 5 : 4
Time take by car A to cover that distance => 5x = 40   x= 8 minutes
  Time taken by car B to cover the distance = 4x =4 x 8 =32 minutes
10. A girl travels wit the speed $\frac{2}{7}$ of her original speed, she reaches her school  25 minutes late, then time taken by her  with her original speed is
        a)    10 minutes   b)15 minutes   c)40 minutes      d)1 hour
Answer : A
Explanation : Let the usual time be t minutes
   When time speed decreases to
2 / 7
of her usual speed, time taken will increase to
7 / 2
th of her usual time.
Ratio of times taken by her at reduced speed  and original  speed = 7 : 2
         Difference of times = 7x-2x = 5x = 25 minutes
   Time taken at original speed= 2x = 10 minutes

11. A person travels $\frac{3}{7}$th of his journey at 30 kmph and remaining $\frac{4}{7}$th journey at 20 kmph. If the total distance travelled is 210km , what is his average speed for the whole journey?
a)22 kmph    b)25 kmph    c)27.65 kmph    d)23.33 kmph
Answer : C
Explanation : 
3 / 7
th his journey = 210 x
3 / 7
= 90 km
 He travelled 90 km at 30 kmph => Time taken to travel 90 km =
90 / 30
= 3 hours.
    Remaining
4 / 7
th of journey = 210 x
4 / 7
= 120 km
 He covered 120km at 40 kmph=> Time taken to travel 120km =
120 / 20
=6 hours
    Total distance = 210 km             Total time= 9 hours
         Average Speed =
Total Distance / Total Time
      =
210 / 9
=23.3 kmph
12. The ratio of the speed a car to that or a motorbike is 5:7. Also a bus covered a distance of 840km in 12 hours. The speed of the car is 4/7th the speeds of the bus.How much distance will the motorbike cover in 6 hours?
a)300 km      b)336 km      c)420 km             d)475 km
Answer :B
Explanation : Distance travelled by bus= 840 km and time= 12 hours
 Speed of bus=
Distance / Time
=
840 / 12
= 70 kmph
Now  Speed of car=
4 / 7
th the speed of car =
4 / 7
x 70 = 40 kmph
      Ratio of speed of car and motorbike= 5:7
              Speed of car= 5x=40
           Then speed of motorbike=7x=7x8 = 56kmph
  Distance covered by motorbike in 9 hours
= Speed x Time
   = 56 x 6 = 336
13. A person covers a distance of 72 km in 9 hours on motorbike. How much distance will the person cover on car  in 5 hours, if he drives the car at 4 times the speed of the motorbike?
a)120 km      b)135 km      c)150 km      d)160km
Answer :D
Explanation : Distance covered by person on motorbike = 72 km and Time taken by him= 9 hours
Therefore speed of motorbike=
Distance / Time
=
72 / 9
= 8 kmph
   He drives the car with 4 times the speed of the motorbike => Speed of the car= 4 x 8 =32 kmph
  Distance covered by him by car in 5 hours = Speed X Time = 32 x5 =160km.

14.  The average speed of a single stop train is 87 kmph. The train was scheduled to start at 9 a.m in bengalore, and  as per schedule it has to reach a destination of 348 km away from  bengalore at 1:45 p.m same day and a halt was scheduled on the way . For how long was the halt scheduled?    
   a)    45 minutes               b)1 hour                     c)90 minutes           d) 2 hour 30 minutes
Answer : A
Explanation : Speed of train = 87 kmph and distance it covers is 348 km.
Time taken to cover the distance=
Distance / Speed
= 348/87= 4 hours.
   But total time taken by train to reach destination is = 1:45 pm – 9 a.m =4 hours 45 minutes.
Time of halt = Total time – take taken without halt
= 4 hours 45 minutes – 4 hours = 45 minutes

15. Hritik goes to his office by car at a speed of 40 kmph and reaches 8 minutes earlier. If he goes at a speed of 30 kmph , he reaches 4 minutes late. What is the distance from his house to office?
a)80 km      b)50 km      c)20 km              d)24km
Answer:D
Explanation: 
Let his office time be 10 a.m. He reaches office at 8 minutes earlier when he travels at 40 kmph  => He reaches at 9:52  a.m
He reaches his office 4 minutes late when travels at 30 kmph speed=> He reaches at 10.04 a.m
The time difference is (10.04 – 9.52) = 12 minutes
          Let the distance be D and time=
Distance / Speed
  T1 – T2 = 12 minutes =
12 / 60
hours =
1 / 5
hours
                             
D / 30
D / 40
=
1 / 5
                               
(4D-3D) / 120
=
1 / 5
                                  D= 24 km
16.  Vehicle A covers a certain distance in 8 hours at the speed of 63 kmph. What is the average speed of another vehicle B which travels a distance of 60 km more than the car in the same time?
a)60 kmph    b)70 kmph     c)85 kmph      d)90 kmph
Answer:B
Explanation : Speed of vehicle A = 58 kmph and
                      Time taken by Vehicle A = 5 hours
  Distance travelled by Vehicle A in 5 hours => Distance= Speed x Time
= 58 x 5 =290
        Now distance travelled by vehicle B  = 290+60= 350 km
             Hence speed of vehicle B =
Distance Travelled / Time Taken
                                                 =
350 / 5
= 70  kmph

17.  Ravi drives his car at a speed of 40 kmph and reaches his destination in 5 hours and Ram covers the same distance in 8 hours. If speed of Ravi is increased by 10 kmph and speed of Ram is increased by 15 kmph, what would be the difference between the times taken by them to cover the distance?
  a)    1 hour     b)2 hours   c)45 minutes      d)1.5 hours
Answer: A
Explanation: Distance covered by Ravi at a speed of 40 kmph in 5 hours
ð  Distance= Speed x Time = 40 x 5= 200 km
  Ram covers same distance in 8 hours => Speed of Rama =
Distance / Time
=
200 / 8
= 25 kmph.
  Ravi speed is increased by 10 kmph => New speed of Ravi = 40+10 = 50 kmph
  Ram speed is increased by 15 kmph  =>New speed of Ram = 25+15 = 40 kmph.
     Therefore, time taken by Ravi to cover 200 km at 50 kmph =
200 / 50
= 4 hours
          Time taken by Ram to cover 200 km  at 40 kmph =
200 / 40
= 5 hours
    Required time difference = 5 hours – 4 hours = 1 hour

18.  Average speed of a car is 60 kmph and the average speed of a truck is 25% more than that of car. What is the distance travelled by truck in 6 hours ?
a)    350 km    b)400 km    c)450 km      d)500 km
Answer :C
Explanation : Average speed of car is 60 kmph
     Speed of truck is 25% more than the speed of car.
               Speed of truck =
125 / 100
x 60= 75 kmph
           Distance travelled by truck in 6 hours = Speed of truck x Time
                                                                 =75 x 6 =   450 km
19.  The ratio of speed of a bus, motorbike and car is 5: 9: 6. The speed of the motorbike is 150% the speed of the car . The car can cover a distance of 480 km in 16 hours. What is average speed of bus and motorbike together?
a)25 kmph    b)35 kmph     c)40 kmph      d)45 kmph
Answer :B
Explanation: Let speed of bus , motorbike and car are 5x, 9x  and 6x.
    Speed of the car =
Distance Travelled / Time Taken
= 480/16 = 30 kmph
Now speed of motorbike is 150% of car =>
150 / 100
x 30 = 45 kmph
    Speed of motorbike is 5x=45 =>x= 5 kmph
  Speed of bus=5x =25kmph.
Hence, average speed of bus and motorbike =
Sum of speeds / 2
=
(25+45) / 2
=35 kmph
                                                             

20. A person rides a motor bike at a speed of 75 kmph and covers his journey in 6 hours.By how much the speed will to have increase if the same distance is to be covered in 5 hours ?
a)   15 kmph        b)20 kmph        c)25 kmph   d)28 kmph
Answer : A
Explanation :  Intial speed of motorbike= 75 kmph and time taken to cover the distance=6 hours
Therefore , total distance covered = Speed x Time = 75 x 6 =450 km
 To cover the same distance of 450 km in 5 hours, speed must be =>
$\frac{Distance}{Time}$ = $\frac{450}{5}$= 90 kmph

                   Hence, increase in speed = 90-75 = 15 kmph