Problems On Trains - Study Mode

[#21] A train 125 m long passes a man, running at 5 km/hr 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: $$eqalign{
& { ext{Speed}},{ ext{of}},{ ext{the}},{ ext{train}},{ ext{relative}},{ ext{to}},{ ext{man}} cr
& = {frac{{125}}{{10}}} { ext{ m/sec}} cr
& = {frac{{25}}{2}} { ext{ m/sec}} cr
& = {frac{{25}}{2} imes frac{{18}}{5}} { ext{ km/hr}} cr
& = 45,{ ext{km/hr}} cr
& { ext{Let}},{ ext{the}},{ ext{speed}},{ ext{of}},{ ext{the}},{ ext{train}},{ ext{be}},x,{ ext{km/hr}}. cr
& ext{Then, relative speed} = left( {x - 5}
ight),{ ext{km/hr}} cr
& herefore x - 5 = 45 cr
& Rightarrow x = 50,{ ext{km/hr}} cr} $$

[#22] The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
Correct Answer

(C) 245 m

Explanation

Solution: $$eqalign{
& { ext{Speed}} = {45 imes frac{5}{{18}}} ,{ ext{m/sec}} cr
& ,,,,,,,,,,,,,,,,,, = {frac{{25}}{2}} ,{ ext{m/sec}} cr
& { ext{Time}} = 30,{ ext{sec}} cr
& { ext{Let}},{ ext{the}},{ ext{length}},{ ext{of}},{ ext{bridge}},{ ext{be}},x,{ ext{metres}} cr
& { ext{Then}},,frac{{130 + x}}{{30}} = frac{{25}}{2} cr
& Rightarrow 2left( {130 + x}
ight) = 750 cr
& Rightarrow x = 245,m cr} $$

[#23] Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
Correct Answer

(B) 3 : 2

Explanation

Solution: $$eqalign{
& { ext{Let}},{ ext{the}},{ ext{speeds}},{ ext{of}},{ ext{the}},{ ext{two}},{ ext{trains}},{ ext{be}},x,{ ext{m/sec}} cr
& { ext{and}},y,{ ext{m/sec}},{ ext{respectively}}. cr
& { ext{Then,}},{ ext{length}},{ ext{of}},{ ext{the}},{ ext{first}},{ ext{train}} = 27x,{ ext{metres}}, cr
& { ext{and}},{ ext{length}},{ ext{of}},{ ext{the}},{ ext{second}},{ ext{train}} = 17y,{ ext{metres}}. cr
& herefore frac{{27x + 17y}}{{x + y}} = 23 cr
& Rightarrow 27x + 17y = 23x + 23y cr
& Rightarrow 4x = 6y cr
& Rightarrow frac{x}{y} = frac{3}{2} cr} $$

[#24] A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Correct Answer

(B) 240 m
(F) 240 meters

Explanation

Solution: $$eqalign{
& { ext{Speed}} = {54 imes frac{5}{{18}}} ,{ ext{m/sec}} = 15,{ ext{m/sec}} cr
& { ext{Length}},{ ext{of}},{ ext{the}},{ ext{train}} = left( {15 imes 20}
ight){ ext{m}} = 300,{ ext{m}} cr
& { ext{Let}},{ ext{the}},{ ext{length}},{ ext{of}},{ ext{the}},{ ext{platform}},{ ext{be}},x,{ ext{metres}} cr
& { ext{Then}},,frac{{x + 300}}{{36}} = 15 cr
& Rightarrow x + 300 = 540 cr
& Rightarrow x = 240,{ ext{m}} cr} $$

[#25] A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
Correct Answer

(B) 89 sec

Explanation

Solution: $$eqalign{
& { ext{Speed}} = {frac{{240}}{{24}}} ,{ ext{m/sec}} = 10,{ ext{m/sec}} cr
& herefore { ext{Required}},{ ext{time}} cr
& { ext{ = }}, {frac{{240 + 650}}{{10}}} ,{ ext{sec}}. cr
& = 89,sec. cr} $$