 # Time & Distance (7)

1. How many seconds will a 500 meter long train moving with a speed of 63 km/hr, take to cross a man walking with a speed of 3 km/hr in the direction of the train ?
1. 42
2. 50
3. 30
4. 28

Explanation :-

Relative Speed = 63 – 3 = 60 Km/h = 60 *(5/18) = 50/3 m/sec
Time Taken to pass the man = Distance/Speed
= 500/(50/3) = 30 sec

2. A boat covers a distance of 30 km downstream in 2 hours while it takes 6 hours to cover the same distance upstream. How much time the boat will take to cover 90 km in still water?
1. 6 hrs
2. 9 hrs
3. 15 hrs
4. None of these

Explanation :-

Upstream speed = 30/ 6 km/hr = 5km/h
Downstream speed = 30/2 km/hr = 15 km/h
Speed of boat in still water = (5 + 15)/2 = 10 km/hr
Required time = 90/10 = 9 hrs

3. Car A and B travel to a place at a speed of 35 and 55 km/h respectively. If car B takes 3.5 hours less time than A for the journey, the distance of the place is_
1. 300.25 km
2. 400 km
3. 350.565 km
4. 336.875 km
5. None of these

Explanation :-

Speed of Car A = 35 km/h      Speed of Car B = 55 km/h
Let time taken by Car A = t
Speed = Distance/Time
35 = Distance/t       &       55 = Distance/(t-3.5)
Distance = 35t        &       Distance = 55(t-3.5)
Therefore , 35t =  55(t-3.5)
t = 77/8
Distance = 35 * 77/8 = 336.87 km

4. A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is
1. 4:5
2. 9:5
3. 8:5
4. 9:2

Explanation :-

Dog : Hare = (3*3) leaps of hare : 5 leaps of hare = 9 : 5

5. Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
1. 10
2. 15
3. 12
4. 20