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Time and Distance Questions

101. Two cities, A and B, at a distance of 50 km, are connected by two separate roads. The speed of any vehicle traveling between the two cities on road 1 is 50 km/hr, while the speed on road 2 is (80/n) km/hr, where n is the number of vehicles (including the concerned vehicle). If you travel in a vehicle from A to B on road 1 and come back from B to A on road 2 (where there are already three vehicles plying), your approximate average speed is?

Correct Ans:29 km/hr

102. A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current, respectively? 

Correct Ans:8:3

103. A man can row 9 â…“ kmph in still water and finds that it takes him thrice as much time to row up than as to row down the same distance in the river. The speed of the current is?

Correct Ans:4 â…” kmph

104. A man can row three-quarters of a kilometre against the stream in 11¼ minutes and down the stream in 7½ minutes. The speed (in km/hr) of the man in still water is: 

Correct Ans:5
We can write three-quarters of a kilometre as 750 metres,
11¼ minutes = 675 seconds (upstream)
7½ minutes = 450 seconds (downstream)

Speed = Distance/Time

Upstream Speed (a) = (750/675) m/sec = 10/9 m/sec
Downstream Speed (b) = (750/450) m/sec = 5/3 m/sec

Speed of the man in still water = 1/2 (a+b)

Therefore, Speed of the man in still water = 1/2 (10/9 + 5/3) m/sec
= 25/18 m/sec
Convert m/sec to km/hr
= (25/18) x (18/5) km/hr
= 5 km/hr

105. P, Q and R starts simultaneously from A to B. P reaches B, turns back and meet Q at a distance of 11 km from B. Q reached B, turns back and meet R at a distance of 9 km from B. If the ratio of the speeds of P and R is 3:2, what is the distance between A and B?

Correct Ans:99
Let, Distance between A and B = d
Distance travelled by P while it meets Q = d + 11
Distance travelled by Q while it meets P = d – 11
Distance travelled by Q while it meets R = d + 9
Distance travelled by R while it meets Q = d – 9
Here the ratio of speeds of P & Q => SP : SQ = d + 11 : d – 11
The ratio of speeds of Q & R => SQ : SR = d + 9 : d – 9
But given Ratio of speeds of P & R => P : R = 3 : 2
=> d = 1, 99
=> d = 99 satisfies.
Therefore, Distance between A and B = 99.

106. A train with 120 wagons crosses Arun who is going in the same direction, in 36 seconds. It travels for half an hour from the time it starts overtaking Arun (he is riding on the horse) before it starts overtaking Sriram (who is also riding on his horse) coming from the opposite direction in 24 seconds. Do Arun meet Sriram and in how much time (in seconds) after the train has crossed Sriram did they meet?

Correct Ans:3576 sec
Let the length of the train be L metres and speeds of the train Arun and Sriram be R, A and S respectively, then
---------- (i)
and ---------(ii)
From eq.(i) and (ii)
3(R - A ) = 2 (R + K)
R = 3A + 2K
In 30 minutes (i.e 1800 seconds), the train covers 1800R (distance) but the Arun also covers 1800 A (distance) in the same time. Therefore distance between Arun and Sriram, when the train has just crossed Sriram
= 1800 ( R - A) - 24 ( A + K)
Time required =
= (3600 - 24) = 3576 s

107. Two men together start a journey in the same direction. They travel 12 and 20 km/day respectively. After travelling for 8 days the man travelling at 12 km/day doubles his speed and both of them finish the distance in the same time. Find the number of days taken by them to reach the destination. 

Correct Ans:24 days
For distance,
Distance travelled in 8 days by 1st man,
D1 = 12 × 8 = 96 km.
and by 2nd man,
D2 = 20 × 8 = 160 km
For remaining distance, let both take t days
to reach the final destination.
x – 96 = 2 × 12 × t
x – 96 = 24 t .......... (i)
and x – 160 = 20 t ...... (ii)
From (i) and (ii); we get,
x – 96 – x + 160 = 24 t – 20 t
64 = 4 t
t = 16 days.
Total number of days = 16 + 8 = 24 days.

108. A boy travelled by train which moved at the speed of 30 mph. He then boarded a bus which moved at the speed of 40 mph and reached his destination. The entire distance covered was 100 miles and the entire duration of the journey was 3 hours. Find the distance he travelled by bus. 

Correct Ans:40 miles
Let the time taken by man traveling in Train = t
Timetaken by man traveling in Train = 3 - t
Train Distance Speed Time
D 30 t
Bus 100-d 40 3-t

The Entire Distance = 100 miles
Distance = Speed * Time

Total Distance => Speed * Time of Train + Speed * Time of Bus = Entire Distance

=> 30 t + 40 (3 - t) = 100
=> 30 t + 1200 - 40t = 100
=> 30 t - 40 t = 100 -120
=> 10 t => 20
=> t = 20 / 10
=> t = 2

Substituting the value of t in 40(3-t), we get
=> 40(3 -t)
=> 40(3 - 2)
=> 40 (1)
=> 40 miles.

40 miles is the distance travelled by bus.

109. Jake started from point A to point B. 2 hours and 15 minutes later, Paul left A and arrived at B at the same time as Jake. Had both of them started simultaneously from A and B traveling towards each other, they would have met in 120 minutes. How much time (minutes) did it take for the slower one to travel from A to B if the ratio of speed of the faster to slower is 3:1? 

Correct Ans:202.5 minutes
Time taken by Jake to reach point B = Time taken by Paul to reach Point B + 2 hours 15 minutes
Let the Time taken by Paul to reach point B = x --------------â‘ 
Then, Time taken by Jake to reach point B = x + 2 hours 15 minutes
= x + 135 minutes -------------â‘¡
Ratio of speed of the faster to slower = 3:1
Time = Distance/Speed
Ratio of time (faster to slower i.e., Paul:Jake) = D/3x:D/x
= 1/3:1/1
= 1:3
Time taken by Paul = x
Time taken by Jake = 3x
From â‘¡, Time taken by Jake = x + 135 minutes
=> 3x = x + 135
=> 2x = 135
=> x = 67.5
Substituting x = 67.5 in â‘¡,
Time taken by Jake to travel from A to B = 202.5 minutes

110. A train 110 m long is running with speed of 60 km/hr .In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?

Correct Ans:6 sec
Relative speed = Train speed + Man Speed = 60 + 6 = 66 kmph = 18 1/3 m /sec Distance to be covered = 110 meter Time taken = Speed / Distance = 110 / (18 1/3) = (110 / 55) x 3 = 2 x 3 = 6 sec

111. How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? 

Correct Ans:30
Given, Length of the train = 500 m
Speed of the man = 3 km/hr
Speed of the train = 63 km/hr

Time taken by the train to cross a man = Length of the train / (speed of the train – speed of the man)
=> Time = 500 m / (63 – 3) km/hr
=> Time = 500 m / 60 km/hr
(to convert 60 km/hr to m/sec)
=> Time = 500 m / [60 * (5/18) m/sec]
=> Time = {500 / [60 * (5/18)]} sec
=> Time = {(500 * 18) / (60 * 5)} sec
=> Time = 30 sec

112. A train moves past a telegraph post and a bridge 336 m long in 12 seconds and 20 seconds respectively. What is the speed of the train?

Correct Ans:151.2 km/hr

Let the length of the train be x metres and its speed by y m/sec.

Time = Length / Speed of the train

Given,A train moves past a telegraph post in 12 seconds.
Then, x/y = 12
=> x = 12y

Now, the same train moves past a bridge of 336 m long in 20 seconds.
=> (Length of the train + Length of the bridge) /Speed of train =Time taken by train to cross the bridge
=> (x + 336) / y = 20
Subs x = 12y in the above eqn, we get
=> (12y + 336) = 20y
=> 20y - 12y = 336
=> 8y = 336
=> y = 42
--->.ThereforeSpeed of the train= 42 m/sec
Convert m/sec to km/hr
Speed of the train= 42 x (18/5) km/hr
=151.2 km/hr.


113. A train speeds past pole in 15 seconds and a platform 100 m long in 25 seconds ,its length is:

Correct Ans:150 m

114. A 300 m long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds .What is the length of the platform?

Correct Ans:350 m

115. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr ,what is the length of the platform? 

Correct Ans:240 m
Given, time taken by train to pass the man = 20 sec
Speed of the train = 54 km/hr
---> Converting into meter/sec
=> Speed of train =54 * (5/18) m/sec = 15 m/sec

W.K.T: Speed of train = Length of train/ Time taken by train to pass the man
=> 15 =Length of train / 20
=>Length of train = 15 * 20
=>Length of train = 300 metre.

Given,A train passes a station platform in 36 seconds.
=>Speed of train = (Length of train + Length of platform) / Time taken by train to pass the platform
=> 15 = (300 +Length of platform) / 36
=> 15 * 36 = (300+Length of platform)
=> 540 =300+Length of platform
=> 540 - 300 =Length of platform
Thus,Length of platform = 240 meter.

116. A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 seconds .What is the length of the goods train?

Correct Ans:270 m

117. A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel is:

Correct Ans:500 m
Given, Length of the train = 800 m
Speed of the train = 78 km/hr (convert km/hr to m/sec)
= 78 * (5/18) m /sec
= 21.667 m /sec
=> Speed of the train = 21.667 m /sec
Time taken by the train to cross the tunnel = 1 min = 60 sec

To find the length of the tunnel:
Time taken by train to cross tunnel = (Length of tunnel + Length of train) / speed of the train
=> 60 = (Length of tunnel + 800) / 21.667
=> 60 * 21.667 = Length of tunnel + 800
=> 1300 = Length of tunnel + 800
=> 1300 – 800 = Length of tunnel
=> 500 = Length of tunnel
Thus, the Length of tunnel = 500 m

118. The length of the bridge , which a train 130 m long and travelling at 45 km/hr can cross in 30 seconds, is:

Correct Ans:245 m

119. A train 240 m long passed a pole in 24 seconds .How long will it take to pass a platform 650 m long?

Correct Ans:89 sec

120. A train covers a distance of 12 km in 10 minutes .If it takes 6 seconds to pass a telegraph post,then the length of the train is:

Correct Ans:120 m

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