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Memorable Tricks and Rules for solving “Time and Distance” Aptitude Questions:

A. BASIC FORMULAE :

1. Distance =Average speed × time taken

2. Average speed = Distance travelled

time taken

3. Time taken = Distance travelled

Average Speed

4. X km/hour = x × 5

18 meter per second

5. Y meter/second = y × 18

5 kilometer per hour.

B. SHORT CUT FORMULAE FOR TRAIN RELATED PROBLEMS :

TYPE -I

1. The time taken by a train in passing a signal post or a telegraph pole or a main

standing near a railway line

= Length of the train

Speed of the train

2. The time taken by a train in passing a railway bridge or a platform or a tunnel

or a train at rest = m+n

speed

Where, m = length of the train

N= length of the bridge/platform/standing train/tunnel

TYPE –II

1. Time taken by faster train to pass the slower train in the some direction =

m1+m2

x1−x2

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Where, m1 =length of the first train,

m2 = length of the second train,

x1 = speed of the first train,

x2 = speed of the second train

and x1>x 2

2. Time taken by the train to cross the man = m

x−y

Where, both are in the same direction and

m= Length of the train,

x= Speed of the train and

y= Speed of the man

3. Time taken by the train to cross the man running in the opposite direction =

m

x+y

C. TRICKS FOR ‘BOATS AND STREAMS’ RELATED PROBLEMS :

Suppose,

X = Speed of a boat or a man in still water.

Y = Speed of the stream or the current or the river.

Then,

TYPE-I

1. Speed of boat or man with the stream(down stream)

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= Down rate = x+y

2. Speed of boat or man against the stream (Up stream)

= Up rate = x-y

TYPE –II

1. X = 1

2 (Down rate +Up rate)

2. Y= 1

2 (Down rate –Up rate)

D. SPECIAL HINTS :

1. If a body covers a distance at the rate of x and another equal distance at the

rate of y,then

Average Speed = 2xy

x+y

2. If a man changes his speed in the ratio of u : v, then the ratio of the time

taken to cover the same distance is v : m.

PRECAUSTIONS:

1. In a question, unit of all given quantities (speed or distance) will be in the

same manner i.e , either in kilometer per hour (speed) and kilometer

(distance) or in meter per second (speed) and meter (distance)

2. Sometimes we have to change unit of given quantity according to need

of the question. It should be the remembered.

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i) Speed =Distance

Time , Time =

Distance

Speed , Distance = Speed × Time

ii) X km /hr =x × 5

18 m/sec

iii) X m/sec = x × 18

5 km/hr

iv) Suppose a man cover a certain distance at x km/hr and equal

distance at y km / hr. then the average speed during the

Whole journey is [2xy

x+y] km/hr

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