Exercise : 4


1. A train running between two stations A and B arrives at its destination 10 minutes late when its speed is 50 km/h and 50 minutes late when its speed is 30 km/h. What is the distance between the stations A and B ?
(a) 40 km
(b) 50 km
(c) 60 km
(d) 70 km
(e) None of these
Ans.b

Let the distance between the two stations be x km.

Then, x50 - 1060 = x30 - 5060

x50 - 16 = x30 - 56

or x30 - x50 = 23 or x = 50 km

2. A car travels 25 km an hour faster than a bus for a journey of 500 km. If the bus takes 10 hours more than the car, then the speeds of the bus and the car are
(a) 25 km/h and 40 km/h respectively
(b) 25 km/h and 60 km/h respectively
(c) 25 km/h and 50 km/h respectively
(d) 25 km/h and 70 km/h respectively
(e) None of these
Ans.c

Let the speed of the bus be x km / h.

then speed of the car = (x + 25) km / h

\(\frac{500}{x} = \frac{500}{x + 25} + 10\)

⇒ x2 + 25x – 1250 = 0 ⇒ x = 25

Thus speed of the bus = 25 km/h

Speed of the car = 50 km/h

Alternative:

Difference in speeds 25 km / hr is in only option (c).

3. A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 18 seconds. Due to some problem, two boggies were detached. The train now crosses a telegraph post in
(a) 18 sec
(b) 12 sec
(c) 15 sec
(d) 20 sec
(e) None of these
Ans.c

Length of train = 12 × 15 = 180 m.

Then, speed of train = 18018 = 10 m/s

Now, length of train = 10 × 15 = 150m

∴ Required time = 15010 = 15 sec.

4. A man started running at a distance of 225 metre from the train. If the speed of the man is 6 km/h, then how much time should the train wait so that the man will be just able to catch it ?
(a) 214 min
(b) 3 min
(c) 414 min
(d) 412 min
(e) None of these
Ans.a

Time = \(\frac{225}{6 \times \frac{5}{18}}\) = 135 sec = 214 min.

5. A man sitting in a train which is travelling at 50 kmph observes that a goods train, travelling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.
(a) 62 kmph
(b) 58 kmph
(c) 52 kmph
(d) 50 kmph
(e) None of these
Ans.a

Relative speed = (2809) m/sec = (2809 × 185) kmph

= 112 kmph.

∴ Speed of goods train = (112 – 50) kmph = 62 kmph.

6. Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
(a) 2 : 3
(b) 4 : 3
(c) 6 : 7
(d) 9 : 16
(e) None of these
Ans.b

Let us name the trains as A and B. Then,

(A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3.

7. A train 75 metres long overtook a man who was walking at the rate of 6 km/h and passed him in 18 seconds. Again, the train overtook a second person in 15 seconds. At what rate was the second person travelling ?
(a) 3 km/h
(b) 2.5 km/h
(c) 4 km/h
(d) 1.5 km/h
(e) None of these
Ans.a

Let actual speed of train ST km/h.

Then, ST - 6 = 7518 × 185 = 15

⇒ ST = 21 km/h

Now, let speed of second man = Sm

21 - Sm = 7515 × 185 = 18

⇒ Sm = 3 km/h

8. A jogger running at 9 kmph along side a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
(a) 3.6 sec
(b) 18 sec
(c) 36 sec
(d) 72 sec
(e) None of these
Ans.c

Speed of train relative to jogger

= (45 – 9) km/h = 36 km/h

= (36 × 518) m/sec = 10 m/sec

Distance to be covered = (240 + 120) m = 360 m.

∴ Time taken = (36010) sec = 36 sec.

9. Two trains are running at 40 km/h and 20 km/h respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?
(a) 23 m
(b) 2329 m
(c) 27 m
(d) 2779 m
(e) None of these
Ans.d

Relative speed = (40 – 20) km/h

= (20 × 518) m/sec = (509) m/sec

Length of faster train

= (509 × 5) m = 2509m = 2779 m

10. Two trains, 130 and 110 metres long, while going in the same direction, the faster train takes one minute to pass the other completely. If they are moving in opposite direction, they pass each other completely in 3 seconds. Find the speed of trains.
(a) 30 m/s, 40 m/s
(b) 32 m/s, 48 m/s
(c) 40 m/s, 44 m/s
(d) 38 m/s, 42 m/s
(e) None of these
Ans.d

Let speed of trains are S1 m/s and S2 m/s.

Then, s1 - s2 = \(\frac{130 + 110}{60} = 4\) ....(i)

and s1 + s2 = \(\frac{130 + 110}{3} = 80\) ....(ii)

on solving (i) and (ii), we get

S1 = 42 m/s , S2 = 38 m/s