Time and Distance Questions and Answers updated daily – Aptitude

Time and Distance Questions: Solved 288 Time and Distance Questions and answers section with explanation for various online exam preparation, various interviews, Aptitude Category online test. Category Questions section with detailed description, explanation will help you to master the topic.

Time and Distance Questions

81. The speed of a motorboat in upstream is 12 km per hour while river is flowing with a speed of 2 km per hour. If the motorboat takes 3 hours more to travel x km in still water than to travel (x – 24) km in downstream. Find the value of x? 




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Correct Ans:168 km
Explanation:
Let the speed of the motorboat in still water be 'u' km/hr.
Given:
Speed of the river = 2 km/hr
Speed of the motorboat in upstream = 12 km/hr
Upstream speed = u - v
u - v = 12
u - 2 = 12
u = 14 km/hr
Therefore, speed of the motorboat in still water is 14 km/hr.

Downstream speed = u + v
= 14 + 2 = 16 km/hr

WKT, Time = Distance/Speed
As per the question, motorboat takes 3 hours more to travel x km in still water than to travel (x – 24) km in downstream
(x/14) - ((x-24)/16) = 3
(8x - 7(x - 24))/112 = 3
8x - 7x + 168 = 336
x = 168 km.
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82. An airplane flies along the four sides of a square at the speeds of 300, 600, 900 and 1200 km/hr. Find the average speed of the plane around the field. 




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Correct Ans:576 km/hr
Explanation:
Given that an airplane flies along the four sides of a square at the speeds of 300, 600, 900 and 1200 km/hr.

Let the sides of the square be 'a' km.
WKT, Time = Distance/Speed
Time taken for 1st side = a/300
Time taken for 2nd side = a/600
Time taken for 3rd side = a/900
Time taken for 4th side = a/1200

Average speed = Total distance/Total time
Here, Total distance travelled = 4a
Therefore, Average speed = 4a/[(a/300) + (a/600) + (a/900) + (a/1200)]
Average speed = 4a/a[(1/300) + (1/600) + (1/900) + (1/1200)]
Average speed = 4/[(12 + 6 + 4 + 3)/3600]
Average speed = 576 km/hr.
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83. Two ants start simultaneously from two ant holes towards each other. The first ant covers 8% of the distance between the two ant holes in 3 hours, the second ant covered 7/120 of the distance in 2 hours 30 minutes. Find the speed (feet/h) of the second ant if the first ant travelled 800 feet and meet the second ant. 




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Correct Ans:35 feet/hr
Explanation:
Let the total distance be 'd'.
WKT, Speed = Distance/Time
Given, first ant cover 8% of distance in 3 hours.
So, the speed of first ant = 8d/(100*3) = 8d/300 feet/hr

Also given, second ant covers 7/120 of distance in 2 hours 30 minutes.
Here, time = 2 hr 30 minutes = 2 (1/2) hr = 5/2 hr
So, speed of second ant = (7d*2)/(120*5) = 7d/300 feet/hr

If the first ant travelled 800 feet and meet the second ant ,
WKT, Time = Distance/Speed
Time taken by first ant = Time taken by second ant
800/ (8d/300) = (d -800)/ (7d/300)
(800*300)/8d = [(d - 800)*300]/7d
800/8 = (d - 800)/7
100 = (d - 800)/7
700 = d - 800
d = 1500 feet
Speed of second ant = 7d/300 = 7(1500)/300 = 35 feet/hr.
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84. In the same time, a car can travel thrice the distance travelled by a bike. If the speed of the bike is 20 km per hour less than that of the car then what will be the difference between distance between them at the end of 5 hours journey if they start simultaneously from a point? 




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Correct Ans:100 km
Explanation:
Let the time be 'x' hrs and distance be 'a' km.
Given that car can travels thrice the distance than a bike.
The distance travelled by bike in 'x' hrs = 'a' km
Then the distance travelled by car in 'x' hrs = '3a' km
WKT, Speed = Distance/Time
(3a/x) - (a/x) = 20 km/hr
2a/x = 20
a/x = 10 km/hr

In 5 hrs of journey, x = 5
a/5 = 10
a = 50 km

Therefore, total distance travelled by bike = a = 50km
Total distance travelled by car = 3a = 3(50) = 150 km

Required difference in difference between car and bike
= 150 - 50
= 100 km.
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85. A person travels for 3 hours at the speed of 25 km/hr and for 2 hours at the speed of 40 km/hr. At the end of it, he finds that he has covered 1/3 of the total distance. At what speed should he travel to cover the remaining distance in 5 hours? 




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Correct Ans:62 km/hr
Explanation:
Given, a person travels 3 hours at 25km/hr.
WKT, Distance = Speed * Time
So, distance travelled by him in 3hrs = 25 * 3 = 75 km
Also given, he travels 2 hours at 40 km/hr.
Therefore, distance travelled by him in 2 hrs = 40*2 = 80 km

Let the total distance travelled be 'x'.
He covered 1/3 of total distance = (75 + 80) = 155 km
1/3 * x = 155
x = 155 *3
x = 465 km
Therefore, remaining distance = 465 -155 = 310 km

To cover the remaining 310 km in 5 hours,
WKT, Speed = Distance/Time
Required speed = 310/5 = 62 km/hr.
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86. Two trains cross each other in 1 minute moving in the same direction at the speeds of 40 kim/hr and 22 km/hr respectively. If the length of the first train is 125 meter, find the length of the second train?




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Correct Ans:175 meters
Explanation:
Given, speed of first train = 40 kim/hr
speed of second train = 22 km/hr
Since the two trains are moving in same direction, speed can be subtracted.
=> Relative speed = Speed of 1st train - Speed of 2nd train
= (40 - 22) km/hr
= 18 km/hr
--> Converting into m/sec
= 18 x (5/18) m/sec
= 5 m/sec
=> Relative speed = 5 m/sec

Given, Time taken to cross each other = 1 minute = 60 seconds
Length of first train = 125 meter
Let the length of other train = X meter

Then, Relative speed = Sum of the Lengths of trains / Time taken in crossing
--> 5 = (X + 125)/60
--> 5 * 60 = (X + 125)
--> 300 = (X + 125)
--> 300 - 125 = X
---> X = 175 meter
Therefore, the length of second train = 175 meter
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87. A train 150m long is running at a speed of 54 km/hr. Find how long will it take for the train to pass a pole ?




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Correct Ans:10 seconds
Explanation:
We know that,
Speed = 54 kmph
= 54 * (5/18) m/sec
=15 m/sec
When a train crosses a pole, it covers its own length
Required time = (150/15)
= 10 seconds
Time taken to pass a pole = 10 seconds.
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88. Prabhat cycled a distance of 240 kilometre at a certain every hour, he would have taken 4 hrs fewer to reach the destination. What was the speed in km/hr at which Prabhat actually cycled?




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Correct Ans:12
Explanation:
Let the original speed of Prabhat be x km/hr.
WKT, Time = Distance/Speed
Accoroding to the question,
(240/x) - (240/(x + 3)) = 4
240[(1/x) - (1/(x + 3))] = 4
240[(x + 3 - x)/x(x + 3)] = 4
[3/x(x + 3)] = 4/240
x(x + 3) = (240*3)/4
x2 + 3x = 180
x2 + 3x - 180 = 0
x2 + 15x -12x -180 = 0
x(x + 15) - 12(x + 15) = 0
(x + 15) (x - 12) = 0
x = -15, 12
x = 12km/hr
Therefore, the original speed of Prabhat = 12 km/hr.
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89. A man travels a distance of 24 km at 6 km/hr, another distance of 24 km at 8 km/hr and third distance of 24 km at 12 km/hr. His average speed for the whole journey (in km/hr) is




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Correct Ans:8
Explanation:
Given, total distance = 24 + 24 + 24 = 72 km/hr
WKT, Time = Distance/ Speed
Total time = (24/6) + (24/8) + (24/12)
= 4 + 3 + 2 = 9 hrs
Average speed = Total distance/Total time
= 72/9 = 8 km/hr.
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90. Two stations are 677 km apart from each other. Train A started at 2 pm at the speed of 59 km/hr and Train B started at 3.30 pm at the speed of 48 km/hr. For which time both the trains cross each other? 




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Correct Ans:7.30 PM
Explanation:
Total distance between the two stations = 677 km
After one and half an hour train A reached 59*(3/2) = 88.5 km
Remaining distance = 677 – 88.5 = 588.5 km
Both the trains cross each other in,
= 588.5/(59 + 48) = 588.5/107
= 5.5 hours = 5 hours 30 min
Both the trains cross each other after 5 hours 30 min, that is,
= 2 + 5. 30 = 7.30 PM
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91. A boat can travel 55 km downstream in 66 min. The ratio of the speed of the boat in still water to the speed of the stream is 4:1. How much time will the boat take to cover 72 km upstream?




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Correct Ans:2 hour 24 min
Explanation:
Given, Downstream distance (D) = 55 km
Downstream Time (T) = 66 min
---> converting time in minutes to hour
---> Downstream Time (T) = (66/60) hour

W.K.T: Speed = Distance/Time
Speed Downstream = (55/66) * 60 = 50 km/hr

Given, Speed of the boat in still water : Speed of the stream = 4: 1
---> Speed of the boat in still water = 4x
---> Speed of the stream = x
W.K.T: Speed Downstream = (Speed of the boat in still water + Speed of stream)
---> Speed Downstream = 4x + x = 50
---> 5x = 50
---> x = 10
Thus, Speed of the boat in still water = 4x = 4 * 10 = 40 km/hr
and, Speed of the stream = x = 10 km/hr

Now, Speed upstream = (Speed of the boat in still water - Speed of the stream)
---> Speed upstream = 40 - 10 = 30 km/hr

Given, Upstream distance = 72 km
Time taken by the boat to cover upstream distance = Upstream distance/ Speed upstream
= 72/30
= 2 (2/5) hr
= 2 hour [(2/5) * 60 mins]
= 2 hour 24 mins
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92. A man rides a car at 50 km/hr and he reaches the destination after 3 hours. If he rides in the bike he reaches the destination after 2 hours, then find the speed of the bike?




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Correct Ans:75 Km/hr
Explanation:
Speed of the car = 50 km/hr, Time = 3 hours
Total distance = S*T = 50*3 = 150 Km
Speed of the bike = D/T = 150/2 = 75 Km/hr
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93. The taxi charges in a city consist of fixed charges and additional charges per kilometer. The fixed charges are for a distance of up to 5 km and additional charges are applicable per kilometer thereafter. The charge for a distance of 10 km is Rs. 350 and for 25 km is Rs. 800. The charge for a distance of 30 km is 




SHOW ANSWER
Correct Ans:Rs.950
Explanation:

Let's take the fixed charges = Rs. x (for the first 5 km)
And the additional charges = Rs. y /km
As per the question,
Charge for distance 10 km = Rs. 350
So for charge for first 5 km is Rs.x and additional charge for next 5 km is Rs. 5y which can be written as follows,
x + 5y = 350 ....(i)

Charge for distance 25 km = Rs. 800
So for charge for first 5 km is Rs.x and additional charge for next 20 km is Rs. 20y which can be written as follows,
x + 20y = 800 ...(ii)

On solving eqn. (i) and (ii), we get
x = 200, y = 30
Therefore, charge for a distance of 30 km = Charge for first 5 km is Rs.x and additional charges for next 25 km is Rs. 25y
= x + 25y
= 200 + 25(30) = Rs. 950

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94. The speed of Tejas express and Rajdhani express is 108 km/hr and 144 km/hr respectively. Tejas express crossed stationary Shatabdi express in 52/3 sec. If the ratio of length of Tejas express, Shatabdi express and Rajdhani express is 6 : 7 : 8. Then in what time, Rajdhani express will cross Tejas express if both are running in the same direction? 




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Correct Ans:56 sec
Explanation:

The ratio of length of Tejas express, Shatabdi express and Rajdhani express is 6 : 7 : 8.
Let the length of Tejas express = 6x meter
Length of Shatabdi express = 7x meter
Length of Rajdhani express = 8x meter

Given that, Tejas express crossed stationary Shatabdi express = 52/3 sec.
Speed of Tejas express = Length of Tejas and Shatabdi/Time
108*(5/18) = (6x + 7x)/(52/3)
13x = (108 *5 *52)/(18*3)
13x = 520
x = 40 meters

Therefore, length of Tejas express = 6*40 = 240 meters
Length of Rajdhani express = 8*40 = 320 meters
Relative speed Tejas and Rajdhani = 144 - 108 = 36 km/hr
= 36 *(5/18) = 10 m/s
Required time to cross each other(Tejas and Rajdhani) = Length of Tejas and Rajdhani/Relative speed
= (240 + 320)/10
= 560/10
= 56 sec.

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95. There is a race of 1 km among Hiten, Vikash and Priyank. Hiten and Vikash run 1 km and Hiten wins by 10 seconds. Hiten and Priyank run 1 km and Hiten wins by 125 mt. When Vikash and Priyank run a km, Vikash wins by 15 seconds. What is the ratio of time taken by Hiten and Vikash to run a km?




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Correct Ans:35:37
Explanation:
If Hiten covers 1 km in x seconds, Vikash covers the same distance in (x +10) seconds.
If Hiten covers 1 km, then in the same time Priyank covers only 875 mt.
If Vikash covers 1 km in (x + 10) sec, then Priyank covers 1 km in (x + 25) sec

Thus in x seconds Priyank covers the distance of 875 mt.
So the speed of Priyank = 875/x
WKT, Time = Distance/Speed
(x + 25) = 1000/(875/x)
x = 175
Time taken by Hiten to complete 1 km = 175 seconds
Time taken by Vikash to complete 1 km = (175 + 10) = 185 seconds
Required ratio of Hiten and Vikash = 175 : 185
= 35 : 37
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96. Salman was travelling on one side of the Yamuna expressway with a constant speed of 120 kmph in his car. Govinda was travelling with a constant speed of 80 kmph in the opposite direction. When they crossed each other, Salman decided to take a U-turn and meet him. But before taking a U turn, Salman had to travel for another 3 minutes. How long will it take for Salman to meet Govinda? [Assume time taken by Salman to take U turn is negligible]




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Correct Ans:18 minutes
Explanation:
Distance Travelled by Salman in 3 minutes = speed * time
= (3/60)*120 = 6 km
Distance travelled by Govinda in 3 minutes = (3/60)*80 = 4 km
Hence, Salman will have to travel totally 10 km distance before catching up with Govinda.
Relative speed of Salman to that of Govinda after taking U turn = 120 - 80 = 40 kmph
Therefore, time taken by Salman after taking U turn = Distance/Relative speed
= 10/40 = 15 minutes
Total time taken by Salman to meet Govinda = time taken for U turn + time taken after U turn
= 3 + 15 = 18 minutes
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97. A train travelling at 48 km/hr crosses another train, having half its length and travelling in opposite direction at 42 km/hr in 12 seconds. It also passed a railway platform in 45 seconds. The length of the rail platform is




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Correct Ans:400 m
Explanation:
Let length of first train be 2L.
And length of second train be L.
Speed of first train = 48 km/hr
Speed of second train = 42 km/hr
WKT, Speed = Distance/Time
(48 + 42)5/18 = (2L + L)/12
(90*5)/18 = 3L/12
L = (25*12)/3
L = 100 m
Therefore, the length of first train = 2*100 = 200 m
Let the length of platform = x
Distance of first train and the platform = 200 + x
Speed of first train = 48 km/hr
First train passes a railway platform in 45 seconds, So
(48 * 5)/18 = (200 + x)/45
600 = 200 + x
x = 400 m
Therefore, length of the platform is 400 m.
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98. The speeds of the Sai and Raj are 50 km/hr and 30 km/hr respectively. Initially Sai is at a place A and Raj is at a place B. The distance between B and A is 710 km. Sai started his journey 3 hours earlier than Raj to meet each other. If they meet each other at a place C somewhere between B and A. Then the distance between C and A is 




SHOW ANSWER
Correct Ans:500 km
Explanation:

Speed of the Sai = 50 km/hr
Total distance = 710 km
WKT, Distance = Speed * Time
Distance covered by Sai in 3 hours = 50 * 3 = 150 km
Remaining distance = 710 – 150 = 560 km
Relative speed = Speed of sai + Speed of Raj
= 50 + 30 = 80 km/hr

They both meet after = Remaining distance/Relative speed
= 560/80 = 7 hours
Now, Sai covers the total distance in = 7 + 3 = 10 hours
Distance covered by Sai in 10 hours = 50 * 10 = 500 km
Distance between C and A = 500 km.


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99. Three persons start walking together and their steps measure 40 cm, 42 cm and 45 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps? 




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Correct Ans:25.2 m
Explanation:
Common Explanation:
The step measure of 3 persons:
P1= 40cm
P2=42cm
P3=45cm
To find the minimum distance, L.C.M should be calculated
L.C.M = 40,42, 45
= 2223357
=2520 cm
Converting cm to m,
2520cm = 25.2m (1m = 100cm)
The minimum distance each should walk to cover the same distance = 25.2m
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100. Two bull started simultaneously towards each other and meet each other 3 hr 20 min later. The ratio of speed of faster bull to that of slower bull is 3 : 1. How much time will it take the slower bull to cover the whole distance? 




SHOW ANSWER
Correct Ans:40/3 hours
Explanation:
Common Explanation:
Let the speed of the slower bull = x
The faster bull is 3 times faster than the slower bull
Therefore, the speed of the faster bull = 3x
The total distance between the bulls:
Distance = Speed*Time
Total distance between the bulls = (3x + x)*(10/3) = 40x/3 km
Time required by the slower bull:
Time = Distance/Speed
Time = 40x/3 / x
Slower Bulls time required = 40/3 hours
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