Model 4 Train Vs Pole/Signal Post/Man Section-Wise Topic Notes With Detailed Explanation And Example Questions

MOST IMPORTANT quantitative aptitude - 6 EXERCISES

Top 10,000+ Aptitude Memory Based Exercises

The following question based on trains topic of quantitative aptitude

Questions : A train, 240 m long crosses a man walking along the line in opposite direction at the rate of 3 kmph in 10 seconds. The speed of the train is

(a) 75 kmph

(b) 83.4 kmph

(c) 86.4 kmph

(d) 63 kmph

The correct answers to the above question in:

Answer: (b)

Using Rule 6,

Let 'a' metre long train is running with the speed 'x' m/s. A man is running in the opposite direction of train with the speed of 'y' m/s. Then, time taken by the train to cross the man = $(a/{(x + y)})$seconds.

If the speed of train be x kmph then,

Its relative speed = (x + 3) kmph

Time = $\text"Length of the train"/ \text"Relative speed"$

$10/3600 = {240/1000}/{(x + 3)} = 240/{1000(x + 3)}$

x + 3 = 86.4 ⇒ x = 83.4 kmph

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Read more crossing pole signal post man Based Quantitative Aptitude Questions and Answers

Question : 1

A 75 metre long train is moving at 20 kmph. It will cross a man standing on the platform in

a) 14 seconds

b) 13.5 seconds

c) 15.5 seconds

d) 12 seconds

Answer: (b)

Using Rule 1,

Speed of train (in m/s)

= 20 × $5/18 = 50/9$ m/sec

Required time = $75/50 × 9$

= 13.5 seconds

Question : 2

A passenger train 150m long is travelling with a speed of 36 km/ hr. If a man is cycling in the direction of train at 9 km/hr., the time taken by the train to pass the man is

a) 15 sec

b) 18 sec

c) 20 sec

d) 10 sec

Answer: (c)

Using Rule 5,
Let 'a' metre long train is running with the speed 'x' m/s. A man is running in same direction and with the speed 'y' m/s, then time taken by the train to cross the man = $a/{(x - y)}$seconds. And a = (x - y)t

Relative speed of train

= (36 - 9) kmph = 27 kmph

= ${27 × 5}/18$ m/sec = $15/2$ m/sec

Required time

= $\text"Length of the train"/ \text"Relative speed"$

= ${150 × 2}/15 = 20$ seconds

Question : 3

A train passes an electrical pole in 20 seconds and passes a platform 250 m long in 45 seconds. Find the length of the train.

a) 200m

b) 300m

c) 250m

d) 400m

Answer: (a)

Using Rule 1,

If the length of train be x metre, then speed of train

= $x/20 = {x + 250}/45$

$x/4 = {x + 250}/9$

9x = 4x + 1000

9x - 4x = 1000

5x = 1000

x = $1000/5$ = 200 metre

Question : 4

If a man walks at the rate of 5 km/hour, he misses a train by 7 minutes. However if he walks at the rate of 6 km/hour, he reaches the station 5 minutes before the arrival of the train. The distance covered by him to reach the station is

a) 7 km

b) 6.25 km

c) 4 km

d) 6 km

Answer: (d)

Let the required distance be x km.

Difference of time = 7 + 5 = 12

minutes = $1/5$ hour

Time = $\text"Distance"/ \text"Speed"$

According to the question,

$x/5 - x/6 = 1/5$

${6x - 5x}/30 = 1/5$

$x/30 = 1/5$ ⇒ $x = 30/5$ = 6 km.

Question : 5

A train, 300m long, passed a man, walking along the line in the same direction at the rate of 3 km/hr in 33 seconds. The speed of the train is

a) 32 km/h

b) 32$8/11$ km/h

c) 35$8/11$ km/h

d) 30 km/h

Answer: (c)

Using Rule 5,

If the speed of the train be x kmph,

then relative speed = (x - 3) kmph.

or (x - 3) × $5/18$ m/sec

$300/{(x - 3) × 5/18 = 33$

5400 = 33 × 5 (x - 3)

360 = 11 (x - 3)

11x - 33 = 360

$x = 393/11 = 35{8}/11$ kmph

Question : 6

A man observed that a train 120 m long crossed him in 9 seconds. The speed (in km/hr) of the train was

a) 45

b) 48

c) 55

d) 42

Answer: (b)

Using Rule 1,

Speed of train

= $120/9 × 18/5$ = 48 kmph

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