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41. Two trains of lenths 120 m and 90 m are running with speed of 80 km/hr and 55 km/hr respectively towards each other on parallel lines. If they are 90 m apart, after how many seconds they will cross each other?

A. 5.6 sec

B. 7.2 sec

C. 8 sec

D. 9 sec

Discuss

Solution:

\begin{aligned} Relative speed \\ =  (80 + 55)km/hr \\ =  135 km/hr \\ = (135 \times \frac{5}{18}) m / \sec \\ = (\frac{75}{2}) m / \sec \\ Distance covered \\ =  (120 + 90 + 90)m \\ =  300m \\ Required time \\ = (300 \times \frac{2}{75}) \sec \\ = 8 \sec \end{aligned}

42. Two trains are coming from opposite directions with speed of 75 km/hr and 100 km/hr on to parallel tracks. At some moment the distance between them is 100km. After T hours, distance between them is again 100 km. T is equal to?

A. 1 hr

B. $1 \frac{1}{7}$ hr

C. $1 \frac{1}{2}$ hr

D. 2 hr

Discuss

Solution:

\begin{aligned} Relative speed \\ =  (75 + 100)km/hr \\ =  175 km/hr \\ Time taken to cover 175 km \\ at relative speed  =  1 hr \\ ∴ T  =  Time taken to cover 200 km \\ = (\frac{1}{175} \times 200) hr \\ = \frac{8}{7} hr \\ = 1 \frac{1}{7} hr \end{aligned}

43. A train, 240 m long, crosses a man walking alone the line in opposite direction at the rate of 3 kmph in 10 seconds. The speed of the train is?

A. 63 kmph

B. 75 kmph

C. 83.4 kmph

D. 86.4 kmph

Discuss

Solution:

\begin{aligned} Speed of the train relative to man \\ = (\frac{240}{10}) m/sec \\ =  24 m/sec \\ = (24 \times \frac{18}{5}) km/sec \\ = \frac{432}{5} km/hr \\ Let the speed of the train be x kmph . \\ Then relative speed  = (x + 3) kmph \\ ∴ x + 3 = \frac{432}{5} \\ \Rightarrow x = \frac{432}{5} - 3 \\ \Rightarrow x = \frac{417}{5} \\ = 83.4 kmph \end{aligned}

44. Two trains of equal length are running on parallel lines in the same directions at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is?

A. 50 m

B. 72 m

C. 80 m

D. 82 m

Discuss

Solution:

\begin{aligned} Let the length of each train be x metres \\ Then distance covered \\ =  2x metres \\ Relative speed \\ =  (46 - 36)km/hr \\ = (10 \times \frac{5}{18}) m / \sec \\ = (\frac{25}{9}) m / \sec \\ ∴ \frac{2 x}{36} = \frac{25}{9} \Leftrightarrow 2 x = 100 \Leftrightarrow x = 50 \end{aligned}

45. Two trains of equal lengths takes 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 miters, in what time ( in seconds) will they cross each other traveling in opposite direction?

A. 10

B. 12

C. 15

D. 20

Discuss

Solution:

\begin{aligned} Speed of the train \\ = (\frac{120}{10}) m/sec \\ =  12 m/sec \\ Speed of the second train \\ = (\frac{120}{15}) m/sec \\ =  8 m/sec \\ Relative speed \\ =  (12 + 8)m/sec \\ =  20 m/sec \\ ∴ Required time \\ = \frac{(120 + 120)}{20} \sec \\ = 12 \sec \end{aligned}

46. A train B speeding with 120 kmph crosses another train C running in the same direction, in 2 minutes. If the lengths of the trains B and C be 100m and 200m respectively, what is the speed (in kmph) of the train C?

A. 111 km

B. 123 km

C. 127 km

D. 129 km

Discuss

Solution:

\begin{aligned} Relative speed of the trains \\ = (\frac{100 + 200}{2 \times 60}) m/sec \\ = (\frac{5}{2}) m/sec \\ Speed of train B \\ =  120 kmph \\ = (120 \times \frac{5}{18}) m/sec \\ = (\frac{100}{3}) m/sec \\ Let the speed of second train be x m/sec \\ Then, \frac{100}{3} - x = \frac{5}{2} \\ \Rightarrow x = (\frac{100}{3} - \frac{5}{2}) \\ = (\frac{185}{6}) m/sec \\ ∴ Speed of second train \\ = (\frac{185}{6} \times \frac{18}{5}) kmph \\ =  111 kmph \end{aligned}

47. What is the speed of a train if it overtakes two persons who are walking in the same direction at the rate of a m/s and (a + 1) m/s and passes them completely in b seconds and (b + 1) seconds respectively?

A. (a + b) m/s

B. (a + b + 1) m/s

C. (2a + 1) m/s

D. $\frac{2 a + 1}{2}$ m/s

Discuss

Solution:

\begin{aligned} Let the length of the train be x metres \\ and its speed be y m/s \\ Then, \\ \frac{x}{y - a} =  b and \\ \frac{x}{y - (a + 1)} = (b + 1) \\ \Leftrightarrow x = b (y - a) and \\ x = (b + 1) (y - a - 1) \\ \Leftrightarrow b (y - a) = (b + 1) (y - a - 1) \\ \Leftrightarrow b y - b a = b y - b a - b + y - a - 1 \\ \Leftrightarrow y = (a + b + 1) \end{aligned}

48. A train passes a 50 meter long platform in 14 seconds and a man standing on platform 10 seconds.The speed of the train is?

A. 24 km/hr

B. 36 km/hr

C. 40 km/hr

D. 45 km/hr

Discuss

Solution:

\begin{aligned} Distance travelled in 14 sec \\ =  50 + l \\ Distance travelled in 10 sec \\ = l \\ So speed of train \\ = \frac{50}{14 - 10} m/sec \\ = \frac{50}{4} \times \frac{18}{5} km/hr \\ =   45 km/hr \end{aligned}

49. A train is moving at a speed of 132 km/hr. If the length of the train is 110 meters, how long it will take to cross a railway platform 165 meter long?

A. 5 second

B. 7.5 second

C. 10 second

D. 15 second

Discuss

Solution:

\begin{aligned} Speed  =  132 km/hr \\ = 132 \times \frac{5}{18} m/sec \\ = \frac{110}{3} m / \sec \\ T = \frac{D}{S} \\ = \frac{110 + 165}{\frac{100}{3}} \\ = \frac{3 (275)}{110} \\ = 7.5 \sec \end{aligned}

50. A train of length 500 feet crosses a platform of length 700 feet in 10 seconds. The speed of the train is?

A. 70 ft/second

B. 85 ft/second

C. 100 ft/second

D. 120 ft/second

Discuss

Solution:

\begin{aligned} Speed of the train \\ = \frac{700 + 500}{10} \\ =  120 ft/second \end{aligned}

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