Direction : Read the following question carefully and choose the right answer.
Important for :
1
The ratio of the speeds of the train and the man is 6 : 1. The length of the train is 650m and crosses a pole in 1 minute 5 seconds. In how much time will the man cross the 240m long platform?
» Explain it
D
Speed of the train = 6x m/s, speed of the man = x m/s

length of the train = 650m,

time taken to cross a pole = 1 minute 5 seconds = 65 seconds

 S = D T

 6x = 650 65

 x = 10 = 5 6 3

 Speed of the man = 5 m/s 3

 Man can cross the 240m platform in 240 5/3

= 144 seconds = 2 minutes 24 seconds

Hence, option D is correct.
2
A train started from point A at a speed of 60 km/hr and after 2 hours another train of same length started from A at a speed of 80 km/hr in the same direction as the first one. After how much time the second train will meet the first train?
» Explain it
C
Let after x hours the second train will meet the first train.

Because distance is same,

S1 t1 = S2 t2

60 (x + 2) = 80 × x

60x + 120 = 80x

80x – 60x = 120

20x = 120

x = 6 hours

Hence, option C is correct.

3
A pilot flies an aircraft at a certain speed for a distance of 800 km. He could have saved 40 min by increasing the average speed of the plane by 40 km/h. Find the average speed of the aircraft.
» Explain it
A
Let the average speed be  a km/hr

 Time taken by aircraft (t) = 800 a

 As per the condition : t – 40 = 800 60 a + 40

 ⇒ 800 – 800 = 2 a a + 40 3

 ⇒ 32000 = 2 a(a + 40) 3

⇒ a( a + 40 ) = 48000

⇒ a = 200Km/hr

Hence option A is correct.

4
A train 125 m long passes a person, running at 8 kmph in the same direction in which the train is going in 25 seconds. The speed of the train is:
» Explain it
D
Speed of the train relative to Person

 = ( 125 ) m/sec = 5 m/sec 25

 ⇒ ( 5 × 18 ) km/hr = 18 km/hr. 5

Let the speed of the train be x kmph. then, relative speed = (x – 8) kmph

So, (x – 8) = 18 ⇒ x = 26 kmph

Hence, option (D) is correct.

5
Two trains of lengths 160 m and 200 m travel at the speeds of 48 m/s and 52 m/s respectively in opposite direction to each other. What is the total time taken by them to cross each other?
» Explain it
A
Relative speed = 48 + 52 = 100 m/s

Total distance covered by both the trains = 160 + 200 = 360 m

 Speed = Distance Time

 ∴   100 = 360 Time

∴   Time = 3.6 seconds

Hence, option A is correct.