Problems On Trains - Study Mode

[#56] A man sitting in a train is counting the pillars of electricity. The distance between two pillars is 60 meters, and the speed of the train is 42 km/hr. In 5 hours, how many pillars will he count?
Correct Answer

(A) 3501

Explanation

Solution: Distance covered by the train in 5 hours = (42 × 5) km = 210 km = 210000 m ∴ Number of pillars counted by the man = $$left( {frac{{210000}}{{60}} + 1}
ight)$$ = 3500 + 1 = 3501

[#57] A 120 meter long train is running at a speed of 90 km/hr. It will cross a railway platform 230 m long in :
Correct Answer

(D) 14 seconds

Explanation

Solution: Speed = $$left( {90 imes frac{5}{{18}}}
ight)$$ xa0 m/sec = 25 m/sec Total distance covered = (120 + 230) m = 350 m ∴ Required time = $$frac{{350}}{{25}}$$ seconds = 14 seconds

[#58] A 50 meter long train passes over a bridge at the speed of 30 km per hour. If it takes 36 seconds to cross the bridge, what is the length of the bridge?
Correct Answer

(B) 250 meters

Explanation

Solution: Speed = $$left( {30 imes frac{5}{{18}}}
ight)$$ xa0m/sec = $$frac{{25}}{3}$$ m/sec Time = 36 second Let the length of the bridge be x meters. Then, $$frac{{50 + { ext{x}}}}{{36}}$$ xa0 = $$frac{{25}}{3}$$ ⇒ 3(50 + x) = 900 ⇒ 50 + x = 300 ⇒ x = 250 meters

[#59] A train takes 5 minutes to cross a telegraphic post. Then the time taken by another train whose length is just double of the first train and moving with same speed to cross a platform of its own length is :
Correct Answer

(C) 20 minutes

Explanation

Solution: Let the length of the train be x metres. Time taken to cover x meters = 5 min = (5 × 60) sec = 300 sec Speed of the train = $$frac{{ ext{x}}}{{300}}$$ m/sec Length of the second train = 2x meters Length of the platform = 2x meters ∴ Required time $$eqalign{
& = left[ {frac{{2{ ext{x}} + 2{ ext{x}}}}{{left( {frac{{ ext{x}}}{{300}}}
ight)}}}
ight]{ ext{sec}} cr
& = left( {frac{{4{ ext{x}} imes 300}}{{ ext{x}}}}
ight){ ext{sec}} cr
& = 1200,{ ext{sec}} cr
& = frac{{1200}}{{60}},{ ext{min}} cr
& = 20,{ ext{minutes}} cr} $$

[#60] A train speeds past a pole in 20 seconds and speeds past a platform 100 meters in length in 30 seconds. What is the length of the train?
Correct Answer

(D) 200 meters

Explanation

Solution: Let the length of the train be x meters and its speed be y m/sec. Then, $$frac{{ ext{x}}}{{ ext{y}}}$$ = 20 ⇒ y = $$frac{{ ext{x}}}{{20}}$$ ∴ $$frac{{{ ext{x}} + 100}}{{30}}$$ xa0= $$frac{{ ext{x}}}{{20}}$$ ⇒ 30x = 20x + 2000 ⇒ 10x = 2000 ⇒ x = 200 meters