Problems On Trains - Study Mode

[#66] A 100 m long train is going at a speed of 60 km/hr. It will cross a 140 m long railway bridge in-
Correct Answer

(C) 14.4 sec

Explanation

Solution: $$eqalign{
& { ext{Speed }} cr
& { ext{ = }}left( {60 imes frac{5}{{18}}}
ight){ ext{m/sec}} cr
& { ext{ = }}frac{{50}}{3}{ ext{ m/sec}} cr
& { ext{Total distance covered}} cr
& { ext{ = (100 + 140) m = 240 m}} cr
& herefore { ext{Required time}} cr
& { ext{ = }}left( {240 imes frac{3}{{50}}}
ight){ ext{sec}} cr
& { ext{ = }}frac{{72}}{5}{ ext{sec}} cr
& { ext{ = 14}}{ ext{.4 sec}} cr} $$

[#67] A train 132 m long passes a telegraph pole in 6 seconds. Find the speed of the train?
Correct Answer

(C) 79.2 km/hr

Explanation

Solution: $$eqalign{
& { ext{Speed}} cr
& { ext{ = }}left( {frac{{132}}{6}}
ight){ ext{m/sec}} cr
& { ext{ = }}left( {22 imes frac{{18}}{5}}
ight){ ext{km/sec}} cr
& { ext{ = 79}}{ ext{.2 km/hr}} cr} $$

[#68] A train running at the speed of 60 kmph crosses a 200 m long platform in 27 seconds. What is the length of the train?
Correct Answer

(C) 250 meters

Explanation

Solution: $$eqalign{
& { ext{Speed}} cr
& { ext{ = }}left( {60 imes frac{5}{{18}}}
ight){ ext{m/sec}} cr
& { ext{ = }}frac{{50}}{3}{ ext{m/sec}} cr
& { ext{Time = 27 sec}}{ ext{.}} cr
& { ext{Let the length of the train be }}x{ ext{ metres}}{ ext{.}} cr
& { ext{Then,}}frac{{x + 200}}{{27}}{ ext{ = }}frac{{50}}{3}{ ext{ }} cr
& Leftrightarrow x + 200 = left( {frac{{50}}{3} imes 27}
ight) = 450 cr
& Leftrightarrow x = 450 - 200 = 250{ ext{ metres}} cr} $$

[#69] A train running at a speed of 90 km/hr crosses a platform double its length in 36 seconds. What is the length of the platform in meters?
Correct Answer

200

Explanation

Solution: $$eqalign{
& { ext{Let the length of the train be x metres}}{ ext{.}} cr
& { ext{Then, length of the platform = (2}}x{ ext{) metres}}{ ext{.}} cr
& { ext{Speed of the train}} cr
& { ext{ = }}left( {90 imes frac{5}{{18}}}
ight)m/sec cr
& = 25m/sec cr
& herefore frac{{x + 2x}}{{25}} = 36 cr
& Rightarrow 3x = 900 cr
& Rightarrow x = 300 cr
& { ext{Hence, length of platform}} cr
& { ext{ = }}2x = left( {2 imes 300}
ight){ ext{m}} = 600{ ext{m}} cr} $$

[#70] A train of length 150 meters takes 40.5 seconds to cross a tunnel of length 300 meters. What is the speed of the train in km/hr?
Correct Answer

(C) 40

Explanation

Solution: $$eqalign{
& { ext{Speed = }}left( {frac{{150 + 300}}{{40.5}}}
ight)m/sec cr
& = left( {frac{{450}}{{40.5}} imes frac{{18}}{5}}
ight)km/hr cr
& = 40km/hr cr} $$