Time and Distance

1. Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds?
   A.9 : 28
   B.11 : 9
   C.11 : 8
   D.9 : 22
   E.None of these
   
   Solution

   Answer – B (11 : 9)
   Explanation – In the same time, they cover 110 km and 90 km respectively.Ratio of their speeds = 110 : 90 = 11 : 9

2. 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.?
A.15
B.8
C.7
D.10
E.None of these

Solution

Answer – C (7)
Explanation – Relative speed = (2 + 3) = 5 rounds per hourSo, they cross each other 5 times in an hour and 2 times in half an hourHence, they cross each other 7 times before 9.30 a.m.

3.The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards 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?
A.10:30 am
B.10:45 am
C.11 am
D.11:25 am
E.None of these

Solution

Answer – C (11 am)
Explanation – Suppose they meet x hrs after 8 a.m.
Then, (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs] = 330
60x + 75(x – 1) = 330
x = 3
So, they meet at (8 + 3), i.e. 11 a.m

4.The speed of a car increases by 2 kms after every one hour. If the distance travelled in the first one hour was 35 kms, what was the total distance traveled in 12 hours?
A.456 kms
B.482 kms
C.552 kms
D.556 kms
E.None of these

Solution

Answer – C (552 kms)
Explanation – Total distance travelled in 12 hours = (35 + 37 + 39 + …… upto 12 terms) This is an A.P. with first term,
a = 35, number of terms, n = 12, common difference, d =2.
Required distance =12/2 (2 x 35 + (12 – 1) x 2) = 6(70 + 22) = 552 kms

5.A thief is noticed by a policeman from a distance of 200 m. 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?
A.100 m
B.150 m
C.190 m
D.200 m
E.None of these

Solution

Answer- A(100m)
Explanation:
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.