Friday, 19 February 2016

Aptitude Questions and Answers - Time and Distance - Concept and Formulae

Time and Distance

Distance :
The length of the path travelled by an object or a body or a person between two places is known as distance. It is measured in meters or kilometres.

Speed :
The distance travelled by any object or person in unit time is knows as speed of the object or speed of a person. It is measured in meter per second or kilometre per hour.
              Speed =
Distance / Time
.
    Distance = Speed x Time
    Time =
Distance / Speed
Example : Sameera travelled a distance of 95 kilometres in 5 hours.
 Therefore distance travelled by her in 1 hour =
95 / 25
= 19 km
               Hence, speed of Sameera = 19kmph

Conversion of Units :
From km/h to m/s :
To convert the speed of an object from kmph to mps , multiply the speed by
5 / 18
.
               X kmph = x x
5 / 18
  mps
Example : 72 kmph = 72 x
5 / 18
= 20 mps

From m/s to km/h.
To convert the speed of an object from mps to kmph, multiply the speed by
18 / 5
.
          X mps= x x
18 / 5
kmph
Example : Convert 30 mps into kmph
           30 x
18 / 5
= 108 kmph
Average Speed :
 It is certain distance is covered in parts at different speeds .
Average speed=
Total Distance Covered / Total Time Taken
 Example :  A person travels 80 km in 6 hours and next 30 km in  5 hours. What is his average speed?
       Total distance covered = 80 km + 30 km  = 110 km
       Total time taken = 6 hours + 5 hours = 11 hours.
 Average Speed =
Total Distance Covered / Total Time Taken
=
110 / 11
= 10 kmph

Average Speed when an object travels equal distances with different speeds:
1.    If a person covers two equal distances with the speed of x and y units  respectively, then the average speed of the man  for complete journey =        
2xy / x+y


Example : John covers a half of the distance with speed of 40 kmph and remaining half of the distance with speed of 60 kmph. What is his average speed?
Answer : He travelled two equal distance with speeds 40kmph and 60kmph
       Average Speed =
2 x 40 x 60 / 40+60


2.    A person travels 3 equal distances with speeds x, y and z units, then his average speed =
3xyz / xy + yz + zx


Example : Sudheer travels
1 / 3
of his journey at 10 km/h , next
1 / 3
at 30km/h and remaining
1 / 3
at 60km/h. What is his average speed during the journey?
a)15 km/h       b)20 km/h   c)25km/h         d)30km/h
Answer :Sudheer travels 3 equal distances at speeds of 10 kmph, 20 kmph and 30 kmph
 Average Speed = 
3xyz / xy + yz + zx
                     =
3 x 10 x 30 x 60 / 10x30 + 30+60 + 60+10
    
                    = 20 kmph

Concept of Relative Speed :
Objects moving in the same direction : If two objects are moving in same direction at  speeds of  x and y , then their relative speed = x-y

For example, if the two bikes A and B move in the same direction at speeds of 520kmph and 40 kmph , then their relative speed of A with respect to B is (50-40)=10 kmph.

Example  : Ravi and Raju start walking in the same direction at 12km/h and 10 km/h respectively. In how many hours will they be 16km apart?
a)4 hours          b)5 hours    c)6 hours       d)8 hours
Answer :    Time =
Distance / Speed
Here both are moving in same direction, so the relative speed is 12-10 = 2 kmph
                Time =
16 / 2
= 8 hours

Objects moving in opposite direction : If two objects are moving in opposite directions at speeds of x and y, then their relative speed = x+y.

If two cars are travelling towards each other at speeds of 30 kmph and 40 kmph respectively, then their relative speed = 30+40 = 70 kmph.

Example : Sameera and Sravani walking in opposite directions at  12km/h and 10 km/h respectively. In how many hours will they be 66 km apart?
a)6 hours      b)33 hours   c)3 hours       d)5 hours
Answer :   Sameera and Sravani are walking in opposite direction , their relative speed is sum of their speeds = 12+10 =22 kmph
          Time =
Distance / Time
=
66 / 22
= 3 hours

Note : The ratio of speeds of two objects is a:b, then to cover same distance, the ratio of time taken will be b:a

Example : The ratio of the speeds of two person to cover a distance is 4:5, then the ratio of time taken by them to cover same distance will be 5 :4.

Example:The ratio between the speeds of A and B is 5 :7 and A takes 35 minutes to cover a distance. In what time does B covers the same distance?
a)10 min   b)15 min    c)25 min                d)30min
Answer : The ratio of between the speeds of A and B is 5:7
   Then ratio of the times taken by A and B = 7:5
   Time taken by A to cover a distance is 7x = 35 minutes
  Therefore, time taken by B to cover same distance = 5x = 5x5 = 25 minutes