Problems On Trains - Study Mode

[#6] A train 100 meter long meets a man going in opposite direction at 5 km/h and passes him in 7 1 / 5 seconds. What is the speed of the train (in km/hr)?
Correct Answer

(A) 45 km/h

Explanation

Solution: $$eqalign{
& { ext{Relative speed of man & train}} cr
& { ext{ = }}frac{{100 imes 5}}{{36}} imes frac{{18}}{5} cr
& { ext{ = 50km/hr}} cr
& herefore { ext{speed of train}} cr
& { ext{ = 50}} - { ext{5}} cr
& { ext{ = 45 km/hr}} cr} $$

[#7] A train takes 9 sec to cross a pole. If the speed of the train is 48 kmph, then length of the train is?
Correct Answer

(B) 120 m

Explanation

Solution: $$eqalign{
& { ext{Time taken by train to cross a pole}} cr
& { ext{ = 9 sec}} cr
& { ext{Distance covered in crossing a pole}} cr
& { ext{ = length of train}} cr
& { ext{Speed of the train}} cr
& { ext{ = 48 km/h}} cr
& = left( {frac{{48 imes 5}}{{18}}}
ight)m/sec cr
& = frac{{40}}{3}m/sec cr
& herefore { ext{Length of the train}} cr
& { ext{ = Speed }} imes { ext{Time}} cr
& { ext{ = }}frac{{40}}{3} imes 9 cr
& { ext{ = 120 m}} cr} $$

[#8] Two trains start at the same time from A and B and proceed toward each other at the sped of 75 km/hr and 50 km/hr respectively. When both meet at a point in between, one train was found to have traveled 175 km more then the other. Find the distance between A and B?
Correct Answer

(A) 875 km

Explanation

Solution: $$eqalign{
& { ext{Let the trains meet after t hours}} cr
& { ext{Speed of train A}} cr
& { ext{ = 75 km/hr}} cr
& { ext{Speed of train B}} cr
& { ext{ = 50 km/hr}} cr
& { ext{Distance covered by train A}} cr
& { ext{ = 75}} imes { ext{t = 75t}} cr
& { ext{Distance covered by train B}} cr
& { ext{ = 50}} imes { ext{t = 50t}} cr
& { ext{Distance}},{ ext{ = Speed }} imes { ext{Time}} cr
& { ext{According to question}} cr
& 75{ ext{t}} - 50{ ext{t}} = 175 cr
& Rightarrow 25{ ext{t}} = 175 cr
& Rightarrow { ext{t}} = frac{{175}}{{25}} = 7,{ ext{hour}} cr
& herefore { ext{Distance between A and B }} cr
& { ext{ = 75t}} + 50{ ext{t}} = 125{ ext{t}} cr
& = 125 imes 7 = 875,{ ext{km}} cr} $$

[#9] Two trains 180 meters and 120 meters in length are running towards each other on parallel tracks, one at the rate 65 km/hr and another at 55 km/hr. In how many seconds will they be cross each other from the moment they meet?
Correct Answer

(B) 9 seconds

Explanation

Solution: $$eqalign{
& { ext{Time taken by trains to cross each }} cr
& { ext{other in opposite direction}} cr
& { ext{ = }}frac{{{l_1} + {l_2}}}{{{ ext{relative speed in opposite direction}}}} cr
& { ext{ = }}frac{{left( {180 + 120}
ight)}}{{left( {65 + 55}
ight)}} cr
& { ext{ = }}frac{{300}}{{120 imes frac{5}{{18}}}} cr
& { ext{ = 9 seconds}} cr} $$

[#10] Two train 100 meters and 95 meters long respectively pass each other in 27 seconds, when they run in the same direction and in 9 seconds when they run in opposite directions. Speed of the two trains are?
Correct Answer

(B) 52 km/hr, 26 km/hr

Explanation

Solution: $$eqalign{
& { ext{Let the speed of first train be }} cr
& {{ ext{S}}_1}{ ext{ km/hr and speed of second train}} cr
& { ext{is }}{{ ext{S}}_2}{ ext{km/hr }} cr
& { ext{As we know,}} cr
& { ext{Time }} cr
& { ext{ = }}frac{{{ ext{total distance}}}}{{{ ext{relative speed in same/opposite direction}}}} cr
& { ext{In the same direction}} cr
& Rightarrow { ext{27 sec = }}frac{{left( {100 + 95}
ight)}}{{left( {{ ext{ }}{{ ext{S}}_1} - { ext{ }}{{ ext{S}}_2}}
ight) imes frac{5}{{18}}}} cr
& Rightarrow 27 = frac{{195 imes 18}}{{left( {{ ext{ }}{{ ext{S}}_1} - { ext{ }}{{ ext{S}}_2}}
ight) imes 5}} cr
& Rightarrow { ext{ }}{{ ext{S}}_1} - { ext{ }}{{ ext{S}}_2} = 26.......................(i) cr
& { ext{In the opposite direction,}} cr
& Rightarrow 9 = frac{{left( {100 + 95}
ight)}}{{left( {{ ext{ }}{{ ext{S}}_1}{ ext{ + }}{{ ext{S}}_2}}
ight) imes frac{5}{{18}}}} cr
& Rightarrow 9 = frac{{195 imes 18}}{{left( {{ ext{ }}{{ ext{S}}_1}{ ext{ + }}{{ ext{S}}_2}}
ight) imes 5}} cr
& Rightarrow { ext{ }}{{ ext{S}}_1}{ ext{ + }}{{ ext{S}}_2} = 39 imes 2 cr
& Rightarrow { ext{ }}{{ ext{S}}_1}{ ext{ + }}{{ ext{S}}_2} = 78 cr
& { ext{From equation (i) and (ii)}} cr
& Rightarrow { ext{ }}{{ ext{S}}_1} - { ext{ }}{{ ext{S}}_2} = 26 cr
& Rightarrow { ext{ }}{{ ext{S}}_1}{ ext{ + }}{{ ext{S}}_2} = 78 cr
& Rightarrow { ext{ }}{{ ext{S}}_1} = frac{{26 + 78}}{2} cr
& Rightarrow { ext{ }}{{ ext{S}}_1} = frac{{104}}{2} cr
& Rightarrow { ext{ }}{{ ext{S}}_1}{ ext{ = 52 km/hr and }} cr
& ,,,,,,,,,,{{ ext{S}}_2}{ ext{ = 26 km/hr}} cr} $$