# Time and Distance - Aptitude Questions and Answers - RejinpaulPlacement

50.
A thief is noticed by a policeman from a distance of 200 km. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes? [S.S.C 2000]

Solution:   Relative speed of the thief and policeman = (11 - 10) km/hr = 1 km/hr.

Distance covered in 6 minutes = [(1/60) * 6] km = 1/10 km = 100 m.

Distance between the thief and policeman = (200 - 100) m = 100 m.

51.
A thief steals a car at 2.30 p.m. and drives it at 60 kmph. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 kmph. When will he overtake the thief? [R.R.B 2002]

Solution:   Suppose the thief is overtaken x hrs after 2.30 p.m.

Then, distance covered by the thief in x hrs
= Distance covered by the owner in [x - (1/2)] hrs.
60 x = 75 [x - (1/2)]
=> 15x = 75/2
=> x = 5/2 hrs.

So, the thief is overtaken at 5 p.m.
52.
Two guns were fired from the same place at an interval of 10 minutes and 30 seconds, but a person in the train approaching the place hears the second shot 10 minutes after the first. The speed of the train (in km/hr), supposing that speed travels at 330 metres per second is:

Solution:   Let the speed of the train be x m/sec.

Then, Distance travelled by the train in 10 min = Distance covered by sound in 30 sec.

=> x * 10 * 60 = 330 * 30
=> x = 16.5

Speed of the train = 16.5 m/sec
= [16.5 * (18/5)] km/hr = 59.4 km/hr
53.
Two cyclist start from the same place in opposite directions. One goes towards north at 18 kmph and the other goes towards south at 20 kmph. What time will they take to be 47.5 km apart?

Solution:   To be (18 + 20) km apart, they take 1 hour.
To be 47.5 km apart, they take [(1/38) * 47.5] hrs = 1   1/4 hrs.
54.
The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels toward B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet? [L.I.C.A.A.O. 2003]

Solution:   Suppose they meet x hrs after 8 a.m.

(Distance moved by first in x hrs) + [Distance moved by second in (x - 1) hrs] = 330

60 x + 75 (x - 1) = 330
=> x = 3.

So, they meet at (8 + 3), i.e., 11 a.m.
55.
The jogging track in a sports complex is 726 metres in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in : [M.A.T 2003

Solution:   Clearly the two will meet when they are 726 m apart.

To be (4.5 + 3.75) = 8.25 km apart, they take 1 hour.

To be 726 m apart, they take [(100/825) * (726/1000)] hrs
= [(242/2750) * 60] min = 528 min.
56.
A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9.30 a.m? [U.P.S.C 2002]