All About Time And Distance

Hello Readers,

Since you all know that Mathematics is one of the most important part of competitive exams, here we posting Some Quick Study Notes on "Time and Distance". We hope that they will help you all in the upcoming competitive exams like SBI PO 2015, Insurance Exams and IBPS CWE 2015. Hope you all like the post..

Introduction:-
The terms time and distance are related to the speed of a moving object.
Speed: Speed is defined as the distance covered by an object in unit time.


Some Important Facts
Distance travelled is proportional to the speed of the object if the time is kept constant.
Distance travelled is proportional to the time taken if speed of object is kept constant.
Speed is inversely proportional to the time taken if the distance covered is kept constant.
If the ratio of two speeds for same distance is a:b then the ratio of time taken to cover the distance is b:a


Relative Speed 
If two objects are moving in same direction with speeds of x and y then their relative speed is (x - y)
If two objects are moving is opposite direction with speeds of x and y then their relative speed is (x + y)


Unit Conversion


Some Important Shortcut Formulas

Rule 1: If some distance is travelled at x km/hr and the same distance is travelled at y km/hr then the average speed during the whole journey is given by


Example
John goes from his home to school at the speed of 2 km/hr and returns at the speed of 3 km/hr. What is his average speed during whole journey in m/sec?
Sol:
Let’s say x = 2 km/hr
And y = 3 km/hr, so



Now, average speed in m/sec
= 2.4*(5/18) = .67m/sec


Rule 2: If a person travels a certain distance at x km/hr and returns at y km/hr, if the time taken to the whole journey is T hours then the one way distance is given by


Example
Mr Samson goes to market at the speed of 10 km/hr and returns to his home at the speed of 15 km/hr. If he takes 3 hours in all, what is the distance between his home and market?
Sol:
Let’s say x = 10 km/hr
y = 10 km/hr, and
T = 3 hrs, then



So the distance between home and market is 18 km.

Rule 3: If two persons A and B start their journey at the same time from two points P and Q towards each other and after crossing each other they take a and b hours in reaching Q and P respectively, then

Example
Two persons Ram and Lakhan start their journey from two different places towards each other’s place. After crossing  each other, they complete their journey in 1 and 4 hours respectively. Find speed of Lakhan if speed of ram is 20 km/hr.
Sol:
Let’s say A = Ram and B = Lakhan
a = 1 and b = 4, then

(20/Lakhan speed)  = (2/1)
Lakhan’s Speed = 10 km/hr

Rule 4: If the same distance is covered at two different speeds S1 and S2 and the time taken to cover the distance are T1 and T2, then the distance is given by


Example
Two trucks travel the same distance at the speed of 50 kmph and 60 kmph. Find the distance when the distance when the time taken by both trucks has a difference of 1 hour.
Sol:
Let’s say S1 = 50 kmph,
S2 = 60 kmph
T1 – T2 =  1

Distance = [(50*60)/(60-50)]*1 = 300km

 Quiz On Time And Distance:-

1.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

2.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

3.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

4.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

5.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

Answers with Explanation:-

1.(c) 
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

2.(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.

3.(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

4.(a)
Let Abhay's speed be x km/hr.
Then, 30/x-30/2x= 3
 6x = 30
 x = 5 km/hr.

5.(c)
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.






1 comment:

  1. Sir,... Tell me about good book for practicing Quantitative Aptitude only for BANK PO/Clerk and SSC. Currently I am using R.S. Aggrawal.

    ReplyDelete