Quant Quiz-Time and distance

1.Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction?
a.15 hours
b.16 hours
c.17 hours
d.18 hours
e.None of these
2. 2 trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds ?
e.None of these

3. A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km?
a.200 Km
b.222 Km
c.224 Km
d.248 Km
e.None of these
4. A Man travelled a distance of 61 km in 9 hours. He travelled partly on foot at 4 km/hr and partly on bicycle at 9 km/hr. What is the distance travelled on foot?
a.16 km
b.14 km
c.12 km
d.10 km
e.None of these
5.If a train runs at 40 km/hour, it reaches its destination late by 11 minutes. But if it runs at 50 km/hour, it is late by 5 minutes only. The correct time (in minutes) for the train to complete the journey is?
e.None of these
6.Busses start from a bus terminal with a speed of 20 km/hr at intervals of 10 minutes. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at intervals of 8 minutes?
a.3 km/hr
b.4 km/hr
c.5 km/hr
d.7 km/hr
e.None of these
7.The distance between two cities A and B is 330km. 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 am.
b.10 : 30 am.
c.11 am.
d.11 : 30 am.
e.None of these
8.Two trains are moving on two parallel tracks but in opposite directions. A person sitting in the train moving at the speed of 80 km/hr passes the second train in 18 seconds. If the length of the second train is 1000 m, its speed is?
a.100 km/hr
b.120 km/hr
c.140 km/hr
d.150 km/hr
e.None of these
9.In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay’s speed is?
a.5 kmph  
b.6 kmph
c.6.25 kmph
d.7.5 kmph
e.None of these
10.It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is?
a.2 : 3
b.3: 2
c.3 : 4
d.4 : 3
e.None of these

In this type of questions we need to get the relative speed between them, 
The relative speed of the boys = 5.5kmph-s5kmph
= 0.5 kmph
Distance between them is 8.5 km
Time = Distance/Speed
Time= 8.5km / 0.5 kmph = 17 hrs
We know total distance is 200 Km
If both trains crossed each other at a distance of 110 km then one train covered 110 km and other 90 km [110+90=200km]
So ratio of their speed = 110:90 = 11:9
Let time taken to travel the first half = x hr 
Then time taken to travel the second half = (10 – x) hr 
Distance covered in the the first half = 21x [because, distance = time*speed]
Distance covered in the the second half = 24(10 – x)
Distance covered in the the first half = Distance covered in the the second half
21x = 24(10 – x)
=> 45x = 240
=> x = 16/3
Total Distance = 2*21(16/3) = 224 Km [multiplied by 2 as 21x was distance of half way]
Let the time in which he travelled on foot = x hour
Time for travelling on bicycle = (9 – x) hr
Distance = Speed * Time, and Total distance = 61 km
4x + 9(9-x) = 61
=> 5x = 20
=> x = 4
So distance traveled on foot = 4(4) = 16 km
If the distance be x km, then x/40-x/50=6/60
 x=20 km.
 Required time = (20/40) hour – 11 minutes 
= (1/2×60-11) minutes = 19 minutes 
Distance covered in 10 minutes at 20 kmph = distance covered in 8 minutes at (20+x) kmph 
20× 10/60=8/60(20+x)
200 = 160 + 8x
8x = 40
x=40/8=5 kmph
7.(c) Distance travelled by first train in one hour
= 60 x 1 = 60 km 
Therefore, distance between two train at 9 a.m.
= 330 – 60 = 270 km
Now, Relative speed of two trains = 60 + 75 = 135 km/hr 
Time of meeting of two trains =270/135=2 hrs. 
Therefore, both the trains will meet at 9 + 2 = 11 A.M.
8.(b) Let the speed of second train be x m/s. 
80 km/h = (80×5)/18 m/s
According to the question 1000/(x+(80×5)/18)=18
100 – 18x + 400
 x=666/18 m/s
= 600/18×18/5 km/h = 120 km/h
Let Abhay’s speed be x km/hr.
Then, 30/x-30/2x= 3
 6x = 30
 x = 5 km/hr.
Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120/x+480/y= 8        1/x+4/y=1/15 ….(i)
And, 200/x+400/y=25/3      1/x+2/y=1/24 ….(ii)
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4.

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