Practice Trains in same direction - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) Two trains 180 metres and 120 metres in length are running towards each other on parallel tracks, one at the rate 65 km/ hour and another at 55 km/hour. In how many seconds will they be clear of each other from the moment they meet ?
(a)
(b)
(c)
(d)
Required time
= $\text"Sum of the lengths of trains"/\text"Relative speed"$
Relative speed = 65 + 55 = 120 kmph
= ${120 × 5}/18$ m/sec
Required time = ${180 + 120}/{{120 × 5}/18}$
= ${300 × 18}/{120 × 5}$ = 9 seconds
Q-2) Two trains 125 metres and 115 metres in length, are running towards each other on parallel lines, one at the rate of 33 km/ hr and the other at 39 km/hr. How much time (in seconds) will they take to pass each other from the moment they meet ?
(a)
(b)
(c)
(d)
Relative speed
= (33 + 39) kmph = 72 kmph
= $({72 × 5}/18)$ m/sec. = 20 m/sec.
Time taken in crossing
= $\text"Length of both trains"/ \text"Relative speed"$
= ${125 + 115}/20 = 240/20$
= 12 seconds
Q-3) A goods train starts running from a place at 1 P.M. at the rate of 18 km/hour. Another goods train starts from the same place at 3 P.M. in the same direction and overtakes the first train at 9 P.M. The speed of the second train in km/hr is
(a)
(b)
(c)
(d)
Distance covered by the first goods train in 8 hours = Distance covered by the second goods train in 6 hours.
18 × 8 = 6 × x
$x = {18 × 8}/6 = 24$ kmph
Q-4) A train 'B' speeding with 100 kmph crosses another train C, running in the same direction, in 2 minutes. If the length of the train B and C be 150 metre and 250 metre respectively, what is the speed of the train C (in kmph)?
(a)
(b)
(c)
(d)
Let the speed of train C be x kmph.
Relative speed of B
= (100 – x ) kmph.
Time taken in crossing
= $\text"Length of both trains"/ \text"Relative speed"$
$2/60 = {({150 + 250}/1000)}/{100 – x}$
$1/30 = 2/{5(100 – x)}$
$1/6 = 2/{100 – x}$
100 – x = 12
x = 100 – 12 = 88 kmph.
Q-5) Two trains travel in the same direction at the speed of 56 km/h and 29 km/h respectively. The faster train passes a man in the slower train in 10 seconds. The length of the faster train (in metres) is
(a)
(b)
(c)
(d)
Relative speed
= 56 – 29 = 27 kmph
= $27 × 5/18 = 15/2$ m/sec
Distance covered in 10 seconds
= $15/2$ × 10 = 75 m
Hence, length of train = 75 m.
Q-6) Two trains, 80 metres and 120 metres long, are running at the speed of 25 km/hr and 35 km/hr respectively in the same direction on parallel tracks. How many seconds will they take to pass each other ?
(a)
(b)
(c)
(d)
Relative speed
= 35 – 25 = 10 kmph
= ${10 × 5}/18$ m/sec.
Total length = 80 + 120 = 200 metres
Required time
= $\text"Sum of the length of trains"/ \text"Relative speed"$
= $200/{{10 × 5}/18} = {200 × 18}/{10 × 5}$
= 72 seconds
Q-7) A boy started from his house by bicycle at 10 a.m. at a speed of 12 km per hour. His elder brother started after 1 hr 15 mins by scooter along the same path and caught him at 1.30 p.m. The speed of the scooter will be (in km/hr)
(a)
(b)
(c)
(d)
Let the speed of Scooter be x Distance covered by cycling in 3$1/2$ hours
= Distance covered by scooter in 2$1/4$ hours
$12 × 7/2 = x × 9/4$
$x = {12 × 7 × 2}/9$
= $56/3 = 18{2}/3$ kmph
Q-8) Two trains are running with speed 30 km/hr and 58 km/hr in the same direction. A man in the slower train passes the faster train in 18 seconds. The length (in metres) of the faster train is :
(a)
(b)
(c)
(d)
Relative speed
= (58 – 30) km/hr
= $(28 × 5/18)$ m/sec. = $70/9$ m/sec.
Length of train
= $70/9$ ×18 = 140 metres
Q-9) Two trains, of same length, are running on parallel tracks in the same direction with speed 60 km/hour and 90 km/hour respectively. The latter completely crosses the former in 30 seconds. The length of each train (in metres) is
(a)
(b)
(c)
(d)
When two trains cross each other, they cover distance equal to the sum of their length with relative speed.
Let length of each train = x metre
Relative speed
= 90 – 60 = 30 kmph
= $({30 × 5}/18)$ m/sec.
= $(25/3)$ m/sec.
${2x}/{25/3} = 30$
2x = ${30 × 25}/3$
2x = 250
x = 125 metres
Q-10) The distance between two places A and B is 60 km. Two cars start at the same time from A and B, travelling at the speeds of 35 km/h and 25 km/h, respectively. If the cars run in the same direction, then they will meet after ( in hours)
(a)
(b)
(c)
(d)
Let both cars meet at C after t hours.
Distance covered by car A
= AC = 35t km
Distance covered by car B
= BC = 25t km
AC – BC = AB = 60 km.
35t – 25t = 60
10t = 60
t = $60/10$ = 6 hours