Problems On Trains - Study Mode

[#61] The time taken by a train 180 m long, travelling at 42 kmph, in passing a person walking in the same direction at 6 kmph, will be
Correct Answer

(A) 18 sec

Explanation

Solution: Speed of train relative to man = (42 - 6) kmph = 36 kmph = $$left( {36 imes frac{5}{{18}}}
ight)$$ xa0m/sec = 10 m/sec ∴ Time taken to pass the man = $$frac{{180}}{{10}}$$ sec = 18 sec

[#62] Two trains 200 meters and 150 meters long are running on parallel rails in the same direction at speed of 40 km/hr and 45 km/hr respectively. Time taken by the faster train to cross the slowed train will be:
Correct Answer

(D) 252 seconds

Explanation

Solution: Relative speed = (45 - 40) km/hr = 5 km/hr = $$left( {5 imes frac{5}{{18}}}
ight)$$ xa0m/sec = $$frac{{25}}{{18}}$$ m/sec Total distance covered = Sum of lengths of trains = (200 + 150) m = 350 m ∴ Time taken = $$left( {350 imes frac{{18}}{{25}}}
ight)$$ xa0 sec = 252 seconds

[#63] A train with 90 km/hr crosses a bridge in 36 seconds. Another train 100 meters shorter crosses the same bridge at 45 km/hr. What is the time taken by the second train to cross the bridge?
Correct Answer

(D) 64 seconds

Explanation

Solution: Let the lengths of the train and the bridge be x meters and y meters respectively. Speed of the first train = 90 km/hr = $$left( {90 imes frac{5}{{18}}}
ight)$$ xa0m/sec = 25 m/sec Speed of the second train
= 45 km/hr = $$left( {45 imes frac{5}{{18}}}
ight)$$ xa0m/sec = $$frac{{25}}{2}$$ m/sec Then, $$frac{{{ ext{x}} + { ext{y}}}}{{36}}$$ = 25 ⇒ x + y = 900 ∴ Required time $$eqalign{
& = left[ {frac{{left( {{ ext{x}} - 100}
ight) + { ext{y}}}}{{frac{{25}}{2}}}}
ight]{ ext{sec}} cr
& = left[ {frac{{left( {{ ext{x}} + { ext{y}}}
ight) - 100}}{{frac{{25}}{2}}}}
ight]{ ext{sec}} cr
& = left( {800 imes frac{2}{{25}}}
ight){ ext{sec}} cr
& = 64,{ ext{sec}} cr} $$

[#64] A train 125 m long passes a man, running at 5 kmph in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Correct Answer

(B) 50 km/hr

Explanation

Solution: Speed of the train relative to man $$eqalign{
& = frac{{125}}{{10}}{ ext{m/sec}} cr
& = frac{{25}}{2}{ ext{m/sec}} cr
& = left( {frac{{25}}{2} imes frac{{18}}{5}}
ight){ ext{m/sec}} cr
& = 45,{ ext{km/hr}} cr} $$ Let the speed of the train be x kmph. Then, relative speed = (x - 5) kmph ∴ x - 5 = 45 or x = 50 km/hr

[#65] Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
Correct Answer

(B) 4 : 3

Explanation

Solution: $$eqalign{
& { ext{Let}},{ ext{us}},{ ext{name}},{ ext{the}},{ ext{trains}},{ ext{as}},{ ext{A}},{ ext{and}},{ ext{B}}{ ext{.}},{ ext{Then}}, cr
& left( {{ ext{A's}},{ ext{speed}}}
ight):left( {{ ext{B's}},{ ext{speed}}}
ight) cr
& = sqrt b :sqrt a cr
& = sqrt {16} :sqrt 9 cr
& = 4:3, cr} $$