Exercise : 5


1. A train overtakes two person who are walking in the same direction in which the train is going , at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:
(a) 45 m
(b) 50 m
(c) 54 m
(d) 72 m
(e) None of these
Ans.b

Let actual speed of train = S m /sec

and length of train = L m.

Then, S - \(\frac{2 \times 5}{18} = \frac{L}{9}\)

⇒ 9S = L + 5 ...… (i)

and S - 4 × 518 = L10

⇒ 90S = 9L + 100 .....(ii)

By (i) & (ii), we get L = 50 m.

2. Local trains leave from a station at an interval of 15 minutes at a speed of 16 km/h. A man moving from opposite side meets the trains at an interval of 12 minutes. Find the speed of the man.
(a) 4 km/h
(b) 3.5 km/h
(c) 4.5 km/h
(d) 3 km/h
(e) None of these
Ans.a

Let speed of man = S km/h. Then,

Distance covered in 15 min = Distance covered in 12 min

16 × 1560 = 1260[16 + S]

⇒ 16 + S = 20 ⇒ S = 4 km/h

3. Local trains leave from a station at an interval of 14 minutes at a speed of 36 km/h. A man moving in the same direction along the road meets the trains at an interval of 18 minutes. Find the speed of the man.
(a) 8 km/h
(b) 7 km/h
(c) 6 km/h
(d) 5.8 km/h
(e) None of these
Ans.a

Let speed of man = S km/h. Then,

36 × 1460 = 1860[36 - S] ⇒ 36 – S = 28 ⇒ S = 8 km/h.

4. A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/h. The other one walks at 5.4 km/h. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
(a) 66 km/h
(b) 72 km/h
(c) 78 km/h
(d) 81 km/h
(e) None of these
Ans.d

4.5 km/h = (4.5 × 518) m/sec = 1.25 m/sec.

& 5.4 km/h = (5.4 × 518) m/sec = 1.5 m/sec.

Let the speed of the train be S m/sec.

Then, (S – 1.25) × 8.4 = (S – 1.5) × 8.5

⇒ 8.4S – 10.5 = 8.5S – 12.75 ⇒ 0.1S = 2.25 ⇒ S = 22.5.

∴ Speed of the train = (22.5 × 185) km/h = 81 km/h

5. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
(a) 1 : 3
(b) 3 : 2
(c) 3 : 4
(d) 2 : 1
(e) None of these
Ans.b

Let the speeds of the two trains be S1 m/sec and S2 m/sec respectively. Then, length of the first train = 27S1 metres, and length of the second train = 17S2 metres.

\(\frac{27S_{1} + 17S_{2}}{S_{1} + S_{2}} = 23 \) ⇒ 27S1 + 17S2 = 23S1 + 23S2

⇒ 4S1 = 6S2S1S2 = 32

6. Two trains each of 120 m in length, run in opposite directions with a velocity of 40 m/s and 20 m/s respectively. How long will it take for the tail ends of the two trains to meet each other during the course of their journey :
(a) 20 s
(b) 3 s
(c) 4 s
(d) 5 s
(e) None of these
Ans.c

Relative speed of the trains = (40 + 20) = 60 m/s

Distance = (120 + 120) = 240 m

Time taken by trains to cross each other completely

= 24060 4s

Directions (Qs. 7 - 8): Answer the following questions on the basis of the information given below:

(i) Trains A and B are travelling on the same route heading towards the same destination. Train B has already covered a distance of 220 km before train A started.

(ii) The two trains meet each other 11 hours after the start of train A.

(iii) Had the trains been travelling towards each other (from a distance of 220 km), they would have met after one hour.

7. What is the speed of train B in kmph?
(a) 100
(b) 180
(c) 116
(d) Data inadequate
(e) None of these
Ans.a

Let the speeds of train A and B be VA and VB respectively.

VA - VB = 2201122011 ⇒ VA - VB = 20 ......(i)

VA + VB = 2201 ⇒ VA + VB = 220 .......(ii)

Solving the equations (i) and (ii), we get VA = 120 km/hr and VB = 100 km/hr

8. What is the speed of train A in kmph?
(a) 102
(b) 80.5
(c) 118
(d) Data inadequate
(e) None of these
Ans.e

Let the speeds of train A and B be VA and VB respectively.

VA - VB = 2201122011 ⇒ VA - VB = 20 ......(i)

VA + VB = 2201 ⇒ VA + VB = 220 .......(ii)

Solving the equations (i) and (ii), we get VA = 120 km/hr and VB = 100 km/hr