Problems On Trains - Study Mode

[#51] A train travelling at a speed of 75 mph enters a tunnel 3 1 / 2 miles long. The train is 1 / 4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
Correct Answer

(B) 3 min

Explanation

Solution: $$eqalign{
& { ext{Total}},{ ext{distance}},{ ext{covered}} cr
& = left( {frac{7}{2} + frac{1}{4}}
ight),{ ext{miles}} cr
& = frac{{15}}{4},{ ext{miles}} cr
& herefore { ext{Time}},{ ext{taken}} cr
& = left( {frac{{15}}{{4 imes 75}}}
ight),{ ext{hrs}} cr
& = frac{1}{{20}},{ ext{hrs}} cr
& = left( {frac{1}{{20}} imes 60}
ight),min cr
& = 3,min cr} $$

[#52] A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:
Correct Answer

(C) 500

Explanation

Solution: $$eqalign{
& { ext{Speed}} = left( {78 imes frac{5}{{18}}}
ight),{ ext{m/sec}} cr
& ,,,,,,,,,,,,,,,,,,,, = {frac{{65}}{3}} ,{ ext{m/sec}} cr
& { ext{Time = }},{ ext{1}},{ ext{minute = 60}},{ ext{second}}. cr
& { ext{Let}},{ ext{the}},{ ext{length}},{ ext{of}},{ ext{the}},{ ext{tunnel}},{ ext{be}},x,{ ext{metres}}. cr
& { ext{Then}},, {frac{{800 + x}}{{60}}} = frac{{65}}{3} cr
& Rightarrow 3left( {800 + x}
ight) = 3900 cr
& Rightarrow x = 500 cr} $$

[#53] A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Correct Answer

(B) 350 m

Explanation

Solution: $$eqalign{
& { ext{Speed}} = {frac{{300}}{{18}}} ,{ ext{m/sec}} cr
& ,,,,,,,,,,,,,,,,,,,, = frac{{50}}{3},{ ext{m/sec}} cr
& { ext{Let}},{ ext{the}},{ ext{length}},{ ext{of}},{ ext{the}},{ ext{platform}},{ ext{be}},x,{ ext{metres}}{ ext{.}} cr
& { ext{Then}}, {frac{{x + 300}}{{39}}} = frac{{50}}{3} cr
& Rightarrow 3left( {x + 300}
ight) = 1950 cr
& Rightarrow x = 350,m. cr} $$

[#54] A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
Correct Answer

(B) 150 m

Explanation

Solution: $$eqalign{
& { ext{Let}},{ ext{the}},{ ext{length}},{ ext{of}},{ ext{the}},{ ext{train}},{ ext{be}},x,{ ext{metres}} cr
& ,{ ext{and}},{ ext{its}},{ ext{speed}},{ ext{by}},y,{ ext{m/sec}} cr
& Then,,frac{x}{y} = 15,,,,,, Rightarrow ,,,,,y = frac{x}{{15}} cr
& herefore frac{{x + 100}}{{25}} = frac{x}{{15}} cr
& Rightarrow 15left( {x + 100}
ight) = 25x cr
& Rightarrow 15x + 1500 = 25x cr
& Rightarrow 1500 = 10x cr
& Rightarrow x = 150m cr} $$

[#55] A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
Correct Answer

(D) 79.2 km/hr

Explanation

Solution: $$eqalign{
& { ext{Let}},{ ext{the}},{ ext{length}},{ ext{of}},{ ext{the}},{ ext{train}},{ ext{be}},x,{ ext{metres}} cr
& ,{ ext{and}},{ ext{its}},{ ext{speed}},{ ext{by}},y,{ ext{m/sec}} cr
& { ext{Then}},,frac{x}{y} = 8,,,,,, Rightarrow ,,,,,x = 8y cr
& { ext{Now}},,frac{{x + 264}}{{20}} = y cr
& Rightarrow 8y + 264 = 20y cr
& Rightarrow y = 22 cr
& herefore { ext{Speed}} = 22,{ ext{m/sec}} cr
& ,,,,,,,,,,,,,,,,,,,,,,, = {22 imes frac{{18}}{5}} ,{ ext{km/hr}} cr
& ,,,,,,,,,,,,,,,,,,,,,,, = 79.2,{ ext{km/hr}} cr} $$