Model 5 Train Vs Both platform and a man/a pole Practice Questions Answers Test with Solutions & More Shortcuts

Question : 1 [SSC CPO S.I.2003]

A moving train passes a platform 50 metres long in 14 seconds and a lamp-post in 10 seconds. The speed of the train is

a) 36 km/hr.

b) 40 km/hr.

c) 45 km/hr.

d) 24 km/hr.

Answer: (c)

Rule 10 and Rule 1,

Suppose length of train be x

According to question

${x + 50}/14 = x/10$

14x = 10x + 500

4x = 500

$x = 500/4 = 125 m$

Therefore, speed

=$125/10 × 18/5 = 45$ kmph

Question : 2 [SSC MTS 2013]

Two trains 100 metres and 95 metres long respectively pass each other in 27 seconds when they run in the same direction and in 9 seconds when they run in opposite directions. Speed of the two trains are

a) 52 km/hr, 26 km/hr

b) 36 km/hr. 18 km/hr

c) 40 km/hr, 20 km/hr

d) 44 km/hr, 22 km/hr

Answer: (a)

Let the speed of trains be x

and y metre/sec respectively,

${100 + 95}/{x - y} = 27$

$x - y = 195/27 = 65/9$ ...(i)

Again,

$195/{x + y} = 9$

$x + y = 195/9$ ...(ii)

By equation (i) + (ii)

$2x = 65/9 + 195/9 = 260/9$

$x = 260/{2 × 9} = 130/9$ m/sec.

= $(130/9 × 18/5)$ kmph = 52 kmph

From equation (ii),

$y = 195/9 - 130/9 = 65/9$ m/sec.

= $65/9 × 18/5$ = 26 kmph

Question : 3 [SSC CPO S.I.2008]

A train passes a platform 110 m long in 40 seconds and a boy standing on the platform in 30 seconds . The length of the train is

a) 110 m

b) 220 m

c) 330 m

d) 100 m

Answer: (c)

Rule 10 and Rule 1,

Let the length of the train be x metres.

Speed of train in crossing boy = $x/30$

Speed of train in crossing platform = ${x +110}/40$

According to the question,

${x +110}/40 =x/30$

${x +110}/4 = x/3$

4x = 3x + 330

x = 330 metres

Question : 4 [SSC CGL Prelim 2005]

A train passes a man standing on a platform in 8 seconds and also crosses the platform which is 264 metres long in 20 seconds. The length of the train (in metres) is :

a) 176

b) 175

c) 96

d) 188

Answer: (a)

Rule 10 and Rule 1,

Let length of train be x m

Speed of train = ${x + 264}/20$

Also, speed of train = $x/8$

Obviously, $x/8 = {x + 264}/20$

$x/2 = {x + 264}/5$

5x = 2x + 528

5x - 2x = 528

x = 528 ÷ 3 = 176 m

Question : 5 [SSC CGL Tier-I 2016]

The time for a train of length 110 metre running at the speed of 72 km/hr to cross a bridge of length 132 metre is

a) 12.1 seconds

b) 12.42 seconds

c) 14.3 seconds

d) 9.8 seconds

Answer: (a)

Speed of train = 72 kmph.

= $({72 × 5}/18)$ m./sec. = 20 m./sec.

Required time

= $\text"Length of train and bridge"/ \text"Speed of train"$

= $({110 +132}/20)$ seconds

= $(242/20)$ seconds = 12.1 seconds

IMPORTANT quantitative aptitude EXERCISES

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