# Time & Distance (9)

1. A train leaves Delhi at 6 a.m and reaches chandigarh at 10 a.m. Another train leaves chandigarh at 8 a.m and reaches Delhi at 11.30 a.m. At what time do the two trains cross one another ?
1. 9.26 a.m
2. 9 a.m
3. 8.36 a.m
4. 8.56 a.m
5. 9.56 a.m

Explanation :-

Let the total distance be x km
Therefore , the speed of 1st train = x / 4
The speed of 2nd train = x / 3.5
In 2 hours 1st train covers half of the total distance .
So remaining is only half of the total distance(ie x/2).
Let t be the time taken
Distance = Time * speed
t*x/4 + t*x/3.5 = x/2
t = 14/15 i.e. 56 min
Total time taken = 2 hrs + 56 min
Time they cross each other is 7:56am (5+2.56)

2. A passenger train takes two hours less for a journey of 300km if its speed is increased by 5km/hr from its normal speed. The normal speed is:
1.35 km/hr
2.50 km/hr
3.25 km/hr
4.30 km/hr
5.37Km/hr

Explanation :-

Let,s Suppose the normal speed of train = x km/hr
Increased speed = (x 5) km/hr
(300/ x) – 2 =  [300 / (x + 5)] (300 – 2x) / x = 300 / (x + 5)
(300 – 2x) (x + 5) = 300x
300x – 2(x*x) +1500 -10x = 300
2(x^2) + 10x -1500 = 0
(x^2) + 5x – 750 = 0
x = 25 km/h

3. A thief steals a car and drives it at 15 km/hr. The theft has been discovered after one hour and the owner of the car sets off in another car at 25 km/hr. When will the owner overtake the thief from the starting point?
1.1 hr
2.1.5 hr
3.2 hr
4.2.5 hr
5. 3 hr

Explanation :-

In 1 hour Distance covered by the thief = 15 km
Relative speed =  km/hr
Time Taken to cover this distance at a speed of 10 km/hr   1.5 hr

4. A car travels first half distance between two places with a speed of 40 km/hr and rest of the half distance with a speed of 60 km/hr. The average speed of the car is:
1.48 km/hr
2.37 km/hr
3.44 km/hr
4.45 km/hr
5.42 Km/hr

Explanation :-

Let the total distance covered = x km
Time = Distance / speed , Therefore
Time for First Half = (x/2) / 40
Time for Second Half = (x/2) / 60
Total Time = [(x/2) / 40] + [(x/2) / 60] = 5x/240
Average Speed = Total distance / Total Time
Average Speed =  x / (5x/240)
Average Speed =48 km/h

5.Two identical trains A and B running in opposite direction at same speed take 2 min 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?
1.40 sec
2.50 sec
3.60 sec
4.20 sec
5.30 sec