Problems on Trains - Examples (with Solutions), Logical Reasoning CAT Notes | EduRev

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CAT : Problems on Trains - Examples (with Solutions), Logical Reasoning CAT Notes | EduRev

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1. A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train?

A. 190 metres

B. 160 metres

C. 200 metres

D. 120 metres

 

Answer : Option C

Explanation :

Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s 

Time taken to cross, t = 18 s 

Distance Covered, d = vt = (400/36)× 18 = 200 m 

Distance covered is equal to the length of the train = 200 m

 

2. A train ,130 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is

A. 270 m

B. 245 m

C. 235 m

D. 220 m

 

Answer : Option B

Explanation :

Assume the length of the bridge = x meter

Total distance covered = 130+x meter

total time taken = 30s

speed = Total distance covered /total time taken = (130+x)/30 m/s

=> 45 × (10/36) = (130+x)/30

=> 45 × 10 × 30 /36 = 130+x

=> 45 × 10 × 10 / 12 = 130+x

=> 15 × 10 × 10 / 4 = 130+x

=> 15 × 25 = 130+x = 375

=> x = 375-130 =245

 

3. A train has a length of 150 meters . it is passing a man who is moving at 2 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train.

A. 182 km/hr

B. 180 km/hr

C. 152 km/hr

D. 169 km/hr

 

Answer : Option A

Explanation :

Length of the train, l = 150m 

Speed of the man , Vm= 2 km/hr 

Relative speed, Vr = total distance/time = (150/3) m/s = (150/3) × (18/5) = 180 km/hr 

Relative Speed = Speed of train, Vt - Speed of man (As both are moving in the same direction) 

=> 180 = Vt - 2 

=> Vt = 180 + 2 = 182 km/hr

 

4. A train having a length of 240 m passes a post in 24 seconds. How long will it take to pass a platform having a length of 650 m?

A. 120 sec

B. 99 s

C. 89 s

D. 80 s

 

Answer : Option C

Explanation :

v = 240/24 (where v is the speed of the train) = 10 m/s

t = (240+650)/10 = 89 seconds

 

5. A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 140 m long?

A. 38 sec

B. 35 s

C. 44 sec

D. 40 s

 

Answer : Option D

Explanation :

Speed = 45 km/hr = 45×(10/36) m/s 

= 150/12 = 50/4 = 25/2 m/s

Total distance = length of the train + length of the platform 

= 360 + 140 = 500 meter

Time taken to cross the platform = 500/(25/2) = 500×2/25 = 40 seconds

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