HCR25Q02 Hindusthan Institutions
Problems on trains for a goods train travelling in the opposite
1. A train passes an electric pole in 10 direction to pass him. If the goods train is
seconds and a platform 120 m long in 18 187.5 m long, find its speed.
seconds. Find the length of the train. (a) 40 km/h (b) 25 km/h (c) 35 km/h (d)
(a) 120 m (b) 150 m (c) 100 m (d) 160 m 36 km/h
2. A train 110 m in length travels at 60 km/h. 8. Two trains are moving in opposite
How much time does the train take in directions at speeds of 60 km/h and 90
passing a man walking at 6 km/h against the km/h. Their lengths are 1.10 km and 0.9 km
train? respectively. The time taken by the slower
(a) 20 s (b) 5 s (c) 10 s (d) 6 s train to cross the faster train in seconds is
(a) 36 (b) 49 (c) 45 (d) 48
3. Two trains are 2 km apart and their
lengths are 200 m and 300 m. They are 9. Two trains, 130 m and 110 m long, are
approaching towards each other with a going in the same direction. The faster train
speed of 20 m/s and 30 m/s respectively. takes one minute to pass the other
After how much time will they cross each completely. If they are moving in opposite
other? directions, they pass each other completely
(a) 50 s (b) 100 s (c) 25/3 s (d) 150 s in 3 seconds. Find the speed of each train.
(a) 38 m/s, 36 m/s (b) 42 m/s, 38 m/s (c)
4. A train covers 180 km distance in 4 hours. 36 m/s. 42 m/s (d) None of these
Another train covers the same distance in 1
hour less. What is the difference in the 10. A train after travelling 150 km meets
distances covered by these trains in 1 hour? with an accident and the proceeds with 3/5
(a) 45 km (b) 9 km (c) 40 km (d) None of of its former speed and arrives at its
these destination 8 h late. Had the accident
occurred 360 km further, it would have
5. If a train runs at 40 km/h, it reaches its reached the destination 4 h late. What is the
destination late by 11 minutes but if it runs total distance travelled by the train?
at 50 km/h, it is late by 5 minutes only. The (a) 840 km (b) 960 km (c) 870 km (d) 1100
correct time for the train to complete its km
journey is
(a) 13 min (b) 15 min (c) 19 min (d) 21 11. Two trains of equal length are running on
min parallel tracks in the same direction at 46
km/h and 36 km/h respectively. The faster
6. A 200 m long train passes a 350 m long train passes the slower train in 36 seconds.
platform in 5 s. If a man is walking at a speed The length of each train is
at a speed of 4 m/s along the track and the (a) 50 m (b) 80 m (c) 72 m (d) 82 m
train is 100 m away from him, how much
time will it take to reach the man? 12. A train 300 m long is running at a speed
(a) Less than 1 s (b) 1.04 s (c) More than 2 of 90 km/h. How many seconds will it take to
s (d) Data insufficient cross a 200 m long train running in the
opposite direction at a speed of 60 km/h?
7. A man sitting in a train travelling at the (a) 7 1/5 (b) 60 (c) 12 (d) 20
rate of 50 km/h observes that it takes 9 sec
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HCR25Q02 Hindusthan Institutions
Boats and Streams 19. Speed of boat in standing water is 9
13. A man can row a boat in downstream at km/h and the speed of the stream is 1.5
12 km/h and in upstream at 8 km/h. Find the km/h. a man rows to a place at a distance of
speed of the boat that the man can row in 105km and comes back to the starting point.
still water The total time taken is
(a) 40 km/h (b) 15 km/h (c) 36 km/h (d) (a) 20 h (b) 18 h (c) 16 h (d) 24 km
35 km/h
20. A person can swim at a speed of 9 km/h
14. Vikas can row a certain distance in still water. If the speed of the stream is 6
downstream in 6 hours and return the same km/h, then how long does he take to swim
distance in 9 hours. If the stream flows at the up to a distance of 9 km and return at the
rate of 3 km/h, find the speed of Vikas in still starting point?
water. (a) 2 h (b) 2.5 h (c) 3 3/5 h (d) 3 3/4 h
(a) 30 km/h (b) 25 km/h (c) 15 km/h (d)
36 km/h Races:
21. In a 2km race A gives a start up of 300 m
15. P,Q and R are the three towns on the to B. Despite this, A wins the race by
bank of a river which flows uniformly. Q is 4oom.fidn the ratio of speed of A and B.
equidistant from P and R. I row from P to Q (a) 20:13 (b) 25:14 (c) 27:8 (d) 34:15
and back in 10 hours and I can row from P to
R in 4 hours. Compare the speed of my boat 22. Ina 2 km race A wins over B by 200 m or
in still water with that of the river 20 seconds. B can give a start up 500 m to c
(a) 6:5 (b) 5:9 (c) 3:7 (d) 4:9 in 2 km race. Find out by how much time A
will over c?
16. A motor boat takes 12 hours to go (a) 1 minute 27 sec (b) 2 minute 30 sec (c)
downstream and it takes 24 hours to return 1.5 minute 45 sec (d) 3 minute 55 sec
the same distance. Find the ratio of the
speed of boat in still water to speed of 23. A beats B by 100m in a race of 12oo m
stream and b beats c by 200 m in a race of 1600 m.
(a) 6:1 (b) 9:11 (c) 3:1 (d) 8:5 Approximately by how many meters can AQ
beat C in a race of 9600 m?
17. A motor boat can travel at 10 km/h in (a) 1600m (b) 1800m (c) 1900m (d)
still water. It traveled 91 km downstream in 2400m
a river and then returned, taking altogether
20 hours. Find the rate of flow of the river. 24. In a 100m race, Partham can beat Ishan
(a) 6 km/h (b) 5 km/h (c) 8 km/h (d) 3 by 20m and Ishan can beat Sarthak by 10m.
km/h In the same race, Partham can beat Sarthak
by:
18. A boat travels upstream from B to A and a) 10m b) 30m c) 28m d) 40m
downstream from A to B in 3 hours. If the
speed of the boat in still water is 9 km/h and 25. In a 100m race, A can beat B by 25m and
the speed of the current is 3 km/h, the B can beat C by 4m. In the same race, A can
distance between A and B is beat c by:
(a) 4 km (b) 8 km (c) 6 km (d) 12 km a) 21m b) 26m c) 28m d) 29m
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