Problems On Trains - Study Mode

[#71] A 280 meter long train crosses a platform thrice its length in 50 seconds. What is the speed of the train in km/hr?
Correct Answer

(C) 80.64

Explanation

Solution: $$eqalign{
& { ext{Length of train}} cr
& { ext{ = 280 m }} cr
& { ext{Length of platform}} cr
& { ext{ = (3}} imes { ext{280) m = 840m}} cr
& herefore { ext{Speed of train}} cr
& { ext{ = }}left( {frac{{280 + 840}}{{50}}}
ight)m/sec cr
& = frac{{1120}}{{50}}m/sec cr
& = left( {frac{{1120}}{{50}} imes frac{{18}}{5}}
ight)km/hr cr
& = 80.64,km/hr cr} $$

[#72] A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Correct Answer

(B) 6 sec

Explanation

Solution: $$eqalign{
& { ext{Speed of train relative to man}} cr
& { ext{ = }}left( {60 + 6}
ight){ ext{km/hr}} cr
& = 66,{ ext{km/hr}} cr
& = left( {66 imes frac{5}{{18}}}
ight)m/sec cr
& = left( {frac{{55}}{3}}
ight)m/sec cr
& herefore { ext{Time taken to pass the man}} cr
& = left( {110 imes frac{3}{{55}}}
ight)sec cr
& = 6,sec cr} $$

[#73] Two trains A and B start running together from the same point in the same direction, at the speed of 60 kmph and 72 kmph respectively. If the length of each of the trains is 240 meters, how long will it take for B to cross train A?
Correct Answer

(D) 2 min 24 sec

Explanation

Solution: $$eqalign{
& { ext{Relative speed}} cr
& { ext{ = (72}} - { ext{60) km/hr}} cr
& { ext{ = 12 km/hr}} cr
& = left( {12 imes frac{5}{{18}}}
ight)m/sec cr
& = left( {frac{{10}}{3}}
ight)m/sec cr
& { ext{Total distance covered}} cr
& { ext{ = Sum of lengths of trains}} cr
& { ext{ = (240 + 240) m}} cr
& { ext{ = 480 m}} cr
& { ext{Time taken}} cr
& { ext{ = }}left( {480 imes frac{3}{{10}}}
ight)sec cr
& = 144sec cr
& = 2min ,24sec cr} $$

[#74] Two trains are moving in opposite directions @60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in second is?
Correct Answer

(C) 48

Explanation

Solution: $$eqalign{
& { ext{Relative speed}} cr
& { ext{ = (60 + 90) km/hr}} cr
& { ext{ = }}left( {150 imes frac{5}{{18}}}
ight){ ext{m/sec}} cr
& { ext{ = }}left( {frac{{125}}{3}}
ight){ ext{m/sec}} cr
& { ext{Distance coverd}} cr
& { ext{ = (1}}{ ext{.10 + 0}}{ ext{.9)km}} cr
& { ext{ = 2 km}} cr
& { ext{ = 2000 m}}{ ext{}} cr
& { ext{Required time}} cr
& { ext{ = }}left( {2000 imes frac{3}{{125}}}
ight)sec cr
& = 48{ ext{ sec}}cr} $$

[#75] Two trains of lenths 120 m and 90 m are running with speed of 80 km/hr and 55 km/hr respectively towards each other on parallel lines. If they are 90 m apart, after how many seconds they will cross each other?
Correct Answer

(C) 8 sec

Explanation

Solution: $$eqalign{
& { ext{Relative speed}} cr
& { ext{ = (80 + 55)km/hr}} cr
& { ext{ = 135 km/hr}} cr
& { ext{ = }}left( {135 imes frac{5}{{18}}}
ight)m/sec cr
& = left( {frac{{75}}{2}}
ight)m/sec cr
& { ext{Distance covered}} cr
& { ext{ = (120 + 90 + 90)m}} cr
& { ext{ = 300m}} cr
& { ext{Required time}} cr
& { ext{ = }}left( {300 imes frac{2}{{75}}}
ight)sec cr
& = 8sec cr} $$