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# MATHS (SOLVED IN STEPS) PROBLEMS ON TRAINS - 03

15. A train overtakes two persons who are walking in the same direction to that of the train at 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. What is the length of the train?
A. 62 m                   B. 54 m               C. 50 m               D. 55 m
Explanation :
Let x is the length of the train in meter and v is its speed in kmph
x/9 = ( v-2)(10/36) —(1)
x/10 =( v-4) (10/36) — (2)
Dividing equation 1 with equation 2
10/9 = (v-2)/(v-4)
=> 10v - 40 = 9v - 18
=> v = 22
Substituting in equation 1, x/9 = 200/36 => x = 9×200/36 = 50 m

16. A train is traveling at 48 kmph . It crosses another train having half of its length , traveling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. What is the length of the platform?
A. 500 m                 B. 360 m                 C. 480 m                  D. 400 m
Explanation :
Speed of train1 = 48 kmph
Let the length of train1 = 2x meter
Speed of train2 = 42 kmph
Length of train 2 = x meter (because it is half of train1’s length)
Distance = 2x + x = 3x
Relative speed= 48+42 = 90 kmph = 90×10/36 m/s = 25 m/s
Time = 12 s
Distance/time = speed => 3x/12 = 25
=> x = 25×12/3 = 100 meter
Length of the first train = 2x = 200 meter
Time taken to cross the platform= 45 s
Speed of train1 = 48 kmph = 480/36 = 40/3 m/s
Distance = 200 + y where y is the length of the platform
=> 200 + y = 45×40/3 = 600
=> y = 400 meter

17. A train having a length of 270 meter is running at the speed of 120 kmph . It crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
A. 320 m                  B. 190 m               C. 210 m               D. 230 m
Explanation :
Relative speed = 120+80 = 200 kmph = 200×10/36 m/s
= 500/9 m/s
time = 9s
Total distance covered = 270 + x ,where x is the length of other train
(270+x)/9 = 500/9
=> 270+x = 500
=> x = 500-270 = 230 meter

18. Two trains, each 100 m long are moving in opposite directions. They cross each other in 8 seconds. If one is moving twice as fast the other, the speed of the faster train is
A. 75 km/hr             B. 60 km/hr               C. 35 km/hr             D. 70 km/hr
Explanation :
Total distance covered = 100+100 = 200 m
Time = 8 s
let speed of slower train is v . Then the speed of the faster train is 2v
(Since one is moving twice as fast the other)
Relative speed = v + 2v = 3v
3v = 200/8 m/s = 25 m/s
=> v = 25/3 m/s
Speed of the faster train = 2v = 50/3 m/s = (50/3)×(36/
10) km/hr = 5×36/3 = 5×12 = 60 km/hr

19. Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?
A. 10.30 a.m                  B. 10 a.m               C. 9.10 a.m.             D. 11 a.m
Explanation :
Assume both trains meet after x hours after 7 am
Distance covered by train starting from P in x hours = 20x km
Distance covered by train starting from Q in (x-1) hours = 25(x-1)
Total distance = 110
=> 20x + 25(x-1) = 110
=> 45x = 135
=> x= 3
Means, they meet after 3 hours after 7 am, ie, they meet at 10 am

20. A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
A. 81 km/hr                 B. 88 km/hr                 C. 62 km/hr              D. 46 km/hr
Explanation :
Let x is the length of the train in meter and y is its speed in kmph
x/8.4 = (y-4.5)(10/36) —(1)
x/8.5 = (y-5.4)(10/36) —(2)
Dividing 1 by 2
8.5/8.4 = (y-4.5)/ (y-5.4)
=> 8.4y - 8.4 × 4.5 = 8.5y - 8.5×5.4
.1y = 8.5×5.4 - 8.4×4.5
=> .1y = 45.9-37.8 = 8.1
=> y = 81 km/hr

21. A train , having a length of 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train
A. 10 sec                   B. 8 sec                    C. 6 sec              D. 4 sec
Explanation :
Distance = 110 m
Relative speed = 60+6 = 66 kmph (Since the train and the man are in moving in opposite direction)
= 66×10/36 mps = 110/6 mps
Time = distance/speed = 110
* MATHS (SOLVED IN STEPS ==> Ratio and Proportion
* MATHS (SOLVED IN STEPS ==> Progressions
* MATHS (SOLVED IN STEPS ==> Percentage
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* MATHS (SOLVED IN STEPS ==> Calendar
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* MATHS (SOLVED IN STEPS ==> Simplification
* MATHS (SOLVED IN STEPS ==> Problems on Average
* MATHS (SOLVED IN STEPS ==> HCF & LCM
* MATHS (SOLVED IN STEPS ==> Profit and Loss
* MATHS (SOLVED IN STEPS ==>
* MATHS (SOLVED IN STEPS ==>
* MATHS (SOLVED IN STEPS ==>
* MATHS (SOLVED IN STEPS ==>