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Time and Distance - Solved Questions 1.     Ravi covers a distance of 900 meters in 180 seconds. Find his speed in kmph? a)...

# 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
Explanation : Distance = 900 meters        Time= 180 seconds
Speed =
Distance / Time
=
900 / 180
= 5 m/s.
But speed is asked in kmph , to convert 5 mps into 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 can it cover in 18 seconds?
a)100m                         b)200m                                  c)270m                        d)150m
Explanation : Speed is in kmph, but time is in seconds. So we have to convert the 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 motorbike can cover a distance of 270 km in 5 hours. What is its speed in m/s?
a)  12.5 mps                b)13.3 mps                        c)15 mps                           d)20 mps
Explanation :  Distance is 270 km and time is 5 hours.
Speed =
Distance / Time
=
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 mps

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
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 the car and reaches his school from his house in 20 minutes. What is the distance between the school and the house?
a)    3 km                      b)4 km                             c)5km                              d)6km
Explanation:   Speed of car = 60 kmph.
The boy runs at one fourth the speed of the car Ã¨ Speed of the boy = ¼ x 60 kmph = 15 kmph
Time taken by the 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 a speed of 6 kmph and returns with a speed of 8 kmph on his bicycle. What is his average speed of the whole journey?
a)    6.85 kmph               b)7.5 kmph                       c)5.5 kmph                        d)8 kmph
Explanation: If a person covers two equal distances at speeds 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)
2 x 6 x 8 / (6+8) = 6.8 kmph approximately

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

2 x 50 x 40 / (50+40)
=
400 / 9
kmph
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
Explanation : Time taken to cover 100km =
Distance / Time
=
100 / 20
= 5 hours
Time taken by car to cover next 210 km =
Distance / Time
=
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
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 the 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. If a girl travels with the speed of 2/7th  of her original speed, then she reaches her school  25 minutes late. Find the time taken by her with her original speed.
a)    10 minutes              b)15 minutes                               c)40 minutes                      d)1 hour
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.
The 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
3 / 7
th of his journey at 30 kmph and the remaining
3 / 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
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
3 / 7
th of journey = 210 x
3 / 7
= 120 km
He covered 120km at 20 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 of a motorbike is 5:7. Also, a bus covered a distance of 840km in 12 hours. The speed of the car is
3 / 7
th, the speed 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
Explanation : Distance travelled by bus= 840 km
Time taken by the bus = 12 hours
Speed of the 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=(7 x 8) = 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 a motorbike. How much distance will the person cover on the 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
Explanation : Distance covered by the person on motorbike = 72 km and the 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 x 5) =160km.

14.  The average speed of a single stop train is 87 kmph. The train was scheduled to start at 9 a.m in Bangalore, and as per schedule, it has to reach a destination of 348 km away from  Bangalore at 1:45 p.m the 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
Explanation: Speed of train = 87 kmph and distance it covers is 348 km.
Time taken to cover the distance without stop=
Distance / Speed
=
348 / 87
= 4 hours.
But the total time taken by train to reach the destination is
= (1:45 pm – 9 a.m) =4 hours 45 minutes.
Hence, halt time = (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 the office?
a)80 km                       b)50 km                           c)20 km                            d)24km
Explanation:
Let his office time be 10 a.m. He reaches his 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 he 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 5 hours at the speed of 58 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
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
D = (58 X 5) = 290 km

Now distance travelled by vehicle B  = (290+60)= 350 km
Hence the 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 the speed of Ravi is increased by 10 kmph and the 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
Explanation: Distance covered by Ravi at a speed of 40 kmph in 5 hours
Ã°  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’s speed is increased by 10 kmph => New speed of Ravi = 40+10 = 50 kmph
Ram’s speed is increased by 15 kmph  =>New speed of Ram = 25+15 = 40 kmph.
Therefore,the  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.  The average speed of a car is 60 kmph, and the average speed of a truck is 25% more than that of a car. What is the distance travelled by truck in 6 hours?
a)    350 km                   b)400 km                          c)450 km                          d)500 km
Explanation: Average speed of the car is 60 kmph
The speed of the truck is 25% more than the speed of the car.
Speed of truck =
125 / 100
x 60= 75 kmph
Distance travelled by truck in 6 hours = Speed of the truck x Time
=(75 x 6) =   450 km
19.  The ratio of the 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 the average speed of the bus and motorbike together?
a)25 kmph                   b)35 kmph                        c)40 kmph                            d)45 kmph
Explanation: Let the speed of the bus, motorbike, and car are 5x, 9x, and 6x.
Speed of the car =
Distance travelled by car / 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, the average speed of bus and motorbike =
Sum of the speeds / 2
=
(25+45) / 2
=35 kmph

20. A person rides a motorbike at a speed of 75 kmph and covers his journey in 6 hours.By how much the speed must be increased if the same distance is to be covered in 5 hours?
a)   15 kmph                 b)20 kmph                        c)25 kmph                         d)28 kmph