Practice | Hashtable

81. Two trains are running in opposite directions with the same speed. If the length of each train is 120 meters and they cross each other in 12 seconds, then the speed of each train (in km/hr) is?

A. 10 km/hr

B. 18 km/hr

C. 72 km/hr

D. 36 km/hr

Discuss

Solution:

Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec
So, 2x =

\frac{120 + 120}{12}

⇒ 2x = 20
⇒ x = 10
∴ Speed of each train = 10 m/sec
=

(10 \times \frac{18}{5})

km/hr
= 36 km/hr

82. A 150 m long train crosses a milestone in 15 seconds and a train of same length coming from the opposite direction in 12 seconds. The speed of the other train is?

A. 36 kmph

B. 45 kmph

C. 50 kmph

D. 54 kmph

Discuss

Solution:

Speed of first train =

\frac{150}{15}

m/sec = 10 m/sec
Let the speed of second train be x m/sec
Relative speed = (10 + x) m/sec
∴

\frac{300}{10 + x}

= 12
⇒ 300 = 120 + 12x
⇒ 12x = 180
⇒ x =

\frac{180}{12}

= 15 m/sec
Hence, speed of other train
=

(15 \times \frac{18}{5})

kmph
= 54 kmph

83. A man standing on a platform finds that a train takes 3 seconds to pass him and another train of the same length moving in the opposite direction takes 4 seconds. The time taken by the trains to pass each other will be :

A. $2 \frac{3}{7}$ seconds

B. $3 \frac{3}{7}$ seconds

C. $4 \frac{3}{7}$ seconds

D. $5 \frac{3}{7}$ seconds

Discuss

Solution:

Let the length of each train be x meters
Then, speed of first train =

\frac{x}{3}

m/sec
Speed of second train =

\frac{x}{4}

m/sec
∴ Required time

\begin{aligned} = [\frac{x + x}{(\frac{x}{3} + \frac{x}{4})}] sec \\ = [\frac{2 x}{(\frac{7 x}{12})}] sec \\ = (2 \times \frac{12}{7}) sec \\ = \frac{24}{7} sec \\ = 3 \frac{3}{7} sec \end{aligned}

84. Two trains, 130 and 110 meters long, are going in the same direction. The faster train takes one minute to pass the other completely. If they are moving in opposite directions, they pass each other completely in 3 seconds. Find the speed of the faster train.

A. 38 m/sec

B. 42 m/sec

C. 46 m/sec

D. 50 m/sec

Discuss

Solution:

Let the speeds of the faster and slower trains be x m/sec and y m/sec respectively.
Then,

\frac{240}{x - y}

= 60
⇒ x - y = 4 . . . . . . . . (i)
And,

\frac{240}{x + y}

= 3
⇒ x + y = 80 . . . . . . . . (ii)
Adding (i) and (ii), we get
2x = 84
⇒ x = 42
Putting x = 42 in (i), we get: y = 38
Hence, speed of faster train = 42 m/sec

85. Two identical trains A and B running in opposite directions at same speed take 2 minutes to cross each other completely. The number of bogies of A are increased from 12 to 16. How much more time would they now require to cross each other?

A. 20 sec

B. 40 sec

C. 50 sec

D. 60 sec

Discuss

Solution:

Let the length of each train be x meters and let the speed of each of them by y m/sec
Then,

\frac{2x}{2 y}

= 120
⇒

\frac{x}{y}

= 120 . . . . . . . (i)
New length of train A

= (\frac{16}{12} x) m = (\frac{4 x}{3}) m

∴ Time taken by trains to cross each other

\begin{aligned} = (\frac{x + \frac{4 x}{3}}{2 y}) sec \\ = \frac{7 x}{6 y} \\ = \frac{7}{6} \times \frac{x}{y} \\ = (\frac{7}{6} \times 120) sec \\ = 140 sec \end{aligned}

Hence, difference in times taken
= (140 - 120) sec
= 20 sec