Friday, 29 January 2016

MATHS (SOLVED IN STEPS) PROBLEMS ON TRAINS - (Page -1)

MATHS (SOLVED IN STEPS)
PROBLEMS ON TRAINS - (Page -1)
1. A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train?
A. 190 metres           B. 160 metres     C. 200 metres               D. 120 metres
Answer : Option C
Explanation :
Speed of the train = 40 km/hr
= 40000/3600 m/s
= 400/36 m/s
Time taken to cross = 18 s
Distance Covered = speed× time
= (400/36)× 18
= 200 m
Distance covered is equal to the length of the train = 200 m

2. A train ,130 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is
A. 270 m                      B. 245 m                    C. 235 m                   D. 220 m
Answer : Option B
Explanation :
Assume the length of the bridge = x meter
Total distance covered = 130+x meter
total time taken = 30s
speed = Total distance covered /total time taken = (130+x)/30 m/s
=> 45 × (10/36) = (130+x)/30
=> 45 × 10 × 30 /36 = 130+x
=> 45 × 10 × 10 / 12 = 130+x
=> 15 × 10 × 10 / 4 = 130+x
=> 15 × 25 = 130+x = 375
=> x = 375-130 =245

3. A train has a length of 150 meters . it is passing a man who is moving at 2 km/hr in the same direction of thetrain, in 3 seconds. Find out the speed of the train.
A. 182 km/hr            B. 180 km/hr              C. 152 km/hr             D. 169 km/hr
Answer : Option A
Explanation :
Length of the train, l = 150m
Speed of the man = 2 km/hr
Relative speed = total distance/time = (150/3) m/s
= (150/3) × (18/5) = 180 km/hr
Relative Speed = Speed of train - Speed of man (As both are moving in the same direction)
=> 180 = Speed of train  - 2
=> Speed of train  = 180 + 2 = 182 km/hr

4. A train having a length of 240 m passes a post in 24 seconds. How long will it take to pass a platform having a length of 650 m?
A. 120 sec              B. 99 s              C. 89 s             D. 80 s
Answer : Option C
Explanation :
speed of the train  = 240/24 = 10 m/s
time taken to pass a platform having a length of 650 m
= (240+650)/10 = 89 seconds

5. A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 140 m long?
A. 38 sec                   B. 35 s                C. 44 sec           D. 40 s
Answer : Option D
Explanation :
Speed = 45 km/hr = 45×(10/36) m/s
= 150/12 = 50/4 = 25/2 m/s
Total distance = length of the train + length of the platform
= 360 + 140 = 500 meter
Time taken to cross the platform = 500/(25/2) = 500×2/25 = 40 seconds

6. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 23 seconds, what is the ratio of their speeds?
A. Insufficient data                 B. 3 : 1                  C. 1 : 3                D. 3 : 2
Answer : Option D
Explanation :
Let the speed of the trains be x and y respectively length of train1 = 27x
length of train2 = 17y
Relative speed= x+ y
Time taken to cross each other = 23 s
=> (27x + 17 y)/(x+y) = 23
=> (27x + 17 y) = 23(x+y)
=> 4x = 6y
=> x/y = 6/4 = 3/2
ratio of their speeds=3:2

7. Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. If the faster train passes the slower train in 36 seconds,what is the length of each train?
A. 88                    B. 70                      C. 62                      D. 50
Answer : Option D
Explanation :
Assume the length of each train = x
Total distance covered for overtaking the slower train =
x+x = 2x
Relative speed = 46-36 = 10km/hr = (10×10)/36 = 100/36 m/s
Time = 36 seconds
2x/ (100/36) = 36
=> (2x × 36 )/100 = 36

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