Problems On Trains - Study Mode

[#76] Two trains are coming from opposite directions with speed of 75 km/hr and 100 km/hr on to parallel tracks. At some moment the distance between them is 100km. After T hours, distance between them is again 100 km. T is equal to?
Correct Answer

(B) $$1frac{1}{7}$$ hr

Explanation

Solution: $$eqalign{
& { ext{Relative speed}} cr
& { ext{ = (75 + 100)km/hr}} cr
& { ext{ = 175 km/hr}} cr
& { ext{Time taken to cover 175 km}} cr
& { ext{at relative speed = 1 hr}} cr
& herefore { ext{T = Time taken to cover 200 km}} cr
& { ext{ = }}left( {frac{1}{{175}} imes 200}
ight), ext{hr} cr
& = frac{8}{7}, ext{hr} cr
& = 1frac{1}{7}, ext{hr} cr} $$

[#77] A train, 240 m long, crosses a man walking alone the line in opposite direction at the rate of 3 kmph in 10 seconds. The speed of the train is?
Correct Answer

(C) 83.4 kmph

Explanation

Solution: $$eqalign{
& { ext{Speed of the train relative to man}} cr
& { ext{ = }}left( {frac{{240}}{{10}}}
ight){ ext{m/sec}} cr
& { ext{ = 24 m/sec}} cr
& { ext{ = }}left( {24 imes frac{{18}}{5}}
ight){ ext{ km/sec}} cr
& { ext{ = }}frac{{432}}{5}{ ext{km/hr}} cr
& { ext{Let the speed of the train be x kmph}}{ ext{.}} cr
& { ext{Then relative speed = }}left( {x + 3}
ight){ ext{kmph}} cr
& herefore x{ ext{ + 3 = }}frac{{432}}{5} cr
& Rightarrow x = frac{{432}}{5} - 3 cr
& Rightarrow x = frac{{417}}{5} cr
& ,,,,,,,,,,,,,, = 83.4,{ ext{kmph}} cr} $$

[#78] Two trains of equal length are running on parallel lines in the same directions at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is?
Correct Answer

(A) 50 m

Explanation

Solution: $$eqalign{
& { ext{Let the length of each train be }}x{ ext{ metres}} cr
& { ext{Then distance covered}} cr
& { ext{ = 2x metres}} cr
& { ext{Relative speed}} cr
& { ext{ = (46}} - { ext{36)km/hr}} cr
& { ext{ = }}left( {10 imes frac{5}{{18}}}
ight)m/sec cr
& = left( {frac{{25}}{9}}
ight)m/sec cr
& herefore frac{{2x}}{{36}} = frac{{25}}{9} Leftrightarrow 2x = 100 Leftrightarrow x = 50 cr} $$

[#79] Two trains of equal lengths takes 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 miters, in what time ( in seconds) will they cross each other traveling in opposite direction?
Correct Answer

(B) 12

Explanation

Solution: $$eqalign{
& { ext{Speed of the train}} cr
& { ext{ = }}left( {frac{{120}}{{10}}}
ight){ ext{ m/sec}} cr
& { ext{ = 12 m/sec}} cr
& { ext{Speed of the second train}} cr
& { ext{ = }}left( {frac{{120}}{{15}}}
ight){ ext{ m/sec}} cr
& { ext{ = 8 m/sec}} cr
& { ext{Relative speed}} cr
& { ext{ = (12 + 8)m/sec}} cr
& { ext{ = 20 m/sec}} cr
& herefore { ext{Required time}} cr
& { ext{ = }}frac{{left( {120 + 120}
ight)}}{{20}},sec cr
& = 12,sec cr} $$

[#80] A train B speeding with 120 kmph crosses another train C running in the same direction, in 2 minutes. If the lengths of the trains B and C be 100m and 200m respectively, what is the speed (in kmph) of the train C?
Correct Answer

(A) 111 km

Explanation

Solution: $$eqalign{
& { ext{Relative speed of the trains }} cr
& { ext{ = }}left( {frac{{100 + 200}}{{2 imes 60}}}
ight){ ext{m/sec}} cr
& { ext{ = }}left( {frac{5}{2}}
ight){ ext{m/sec}} cr
& { ext{Speed of train B}} cr
& { ext{ = 120 kmph}} cr
& = left( {120 imes frac{5}{{18}}}
ight){ ext{m/sec}} cr
& { ext{ = }}left( {frac{{100}}{3}}
ight){ ext{m/sec}} cr
& { ext{Let the speed of second train be }}x{ ext{ m/sec}} cr
& { ext{Then, }} frac{{100}}{3} - x = frac{5}{2} cr
& Rightarrow x = left( {frac{{100}}{3} - frac{5}{2}}
ight) cr
& ,,,,,,,,,,,,,, = left( {frac{{185}}{6}}
ight){ ext{m/sec}} cr
& herefore { ext{Speed of second train}} cr
& { ext{ = }}left( {frac{{185}}{6} imes frac{{18}}{5}}
ight){ ext{ kmph}} cr
& { ext{ = 111 kmph}} cr} $$