time & distance Topic-wise Practice Test, Examples With Solutions & More Shortcuts

Time and Distance - Basic Formulas, Shortcuts, Rules, Tricks & Tips - Quantitative Aptitude

Useful For All Competitive Exams Like UPSC, SSC, BANK & RAILWAY

Posted By Careericons Team

Introduction to Time & Distance:

The concepts of time distance are most important in the terms of competitive exams. The basic concept of time and distance is used in solving the question based on motion in a straight line. The applications of time & distance are used to solve the problems related to trains and races.

In such questions, average distance, time/average time taken to cover any distance, and ratio between speeds or taken times by two persons/ things are asked. Other questions include questions based on – reaching some place before or after the scheduled time, covering a part of the distance on foot or on different conveyances.

To understand time & distance concepts clearly, You need to get through with the basics about Motion or Movement, Displacement, Velocity, Conversion of kmph to m/s & m/s to kmph, Speed, Average Speed, & Relative Speed. Simple definitions & explanations are given below read well to get a clear idea about how the time & distance concept works.

What is Motion or Movement?

When a body changes its position with respect to any external stationary body, it is said that the body is in motion or moving with respect to the stationary body. Thus when a body travels from one place to another place, we say that the body is in motion or the body is moving.

To move from point A to point B situated at a distance (D) from point A with some speed (S) by a body takes some time (T).

For example unit of speed can be metre/sec, km/hour, metre/min., km/min., km/day, km/sec, feet/sec, miles/hr etc

What is Displacement?

Displacement is defined as the change in position of an object. It is a vector quantity and has a direction and magnitude. It is represented as an arrow that points from the starting position to the final position.

ie., The action of moving something from its place or position.

For example- If an object moves from A position to B, then the object's position changes.

What is Velocity?

Velocity defines the direction of the movement of the body or the object. Speed is primarily a scalar quantity. Velocity is essentially a vector quantity. It is the rate of change of distance. It is the rate of change of displacement.

ie., The speed of something in a given direction

Difference between Velocity & Speed:

Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement. Put another way, speed is a scalar value, while velocity is a vector.

For example, 50 km/hr (31 mph) describes the speed at which a car is travelling along a road, while 50 km/hr west describes the velocity at which it is travelling.

How to convert kmph to m/s & m/s to kmph?

What is Speed?

Speed is the rate at which distance is covered during the motion. It is measured in terms of distance per unit of time. Unit of speed may have any combination of unit of distance and unit of time in the numrator and denominator respectively.

The distance covered per unit time is called speed. Speed is directly proportional to distance and inversely to time

The relation between time, distance and speed is,

Main Units

• Time : Seconds, minutes, hours
• Distance : meter, kilometer
• Speed : km/ hr, m /sec

What is Average Speed?

Average speed is defined as the ratio of total distance covered to the total time taken by an object.

i.e. Average speed = $\text"Total travelled"/\text"Total time taken"$

If an object travels d₁, d₂, d₃, ..., d_n distances with different speeds s₁, s₂, s₃, ..., s_n in time t₁, t₂, t₃, ..., t_n respectively; then average speed (S_a) is given by

Special Cases of Averages Speed,

we studied that

(i) If with two different speeds s₁ and s₂ the same distance d is covered, then

Average Speed = ${2s_1 . s_2}/{s_1 + s_2}$

(ii) If with three different speeds s₁, s₂ and s₃ the same distance d is covered, then

Average Speed = ${3s_1 . s_2 . s_3}/{s_1 . s_2 + s_2 . s_3 + s_3 . s_1}$

What is Relative Speed?

Generally, when we talk about the speed of a body, we mean the speed of the body with respect to a stationary point (or object), which we have already discussed. In many cases, we need to determine the speed of a body with respect to an independent moving point (or body).

In such cases, we have to take into account the speed of the independent body with respect to which we want to find the speed of another body. The speed of a body 'A' with respect to an independent moving body 'B' is called relative speed of the body A with respect to the body 'B

Formulae of Relative Speed

(i) If two bodies are moving in opposite directions at speeds s₁ and s₂ respectively, then relative speed of any one body with respect to other body is (s₁ + s₂).

(ii) If two bodies are moving in the same direction at speeds s₁ and s₂ respectively, then relative speed of any one body with respect to other body is given by s₁ – s₂, when s1 is greater than s₂ and s₂ – s₁ when s₂ is greater than s₁

Concepts of this Time and Distance topic are used in solving questions based on motion in a straight line, relative motion, circular motion, train and boat etc. In every competitive exam and other equivalent aptitude tests, a minimum of 2 to 4 questions are generally asked each year. So this topic is very important from the point of view of SSC, BANK, IBPS, Railway, UPSC Exams and other equivalent aptitude tests.

"18" - Important Aptitude Rules, Formulas & Quick Tricks to Solve Time and Distance Based Aptitude Problems

In this list of rules, you will get an idea that How to solve all different types & kinds of Time and Distance based aptitude problems asked in various competitive exams like UPSC, SSC, Bank, and Railway examinations at all levels.

By using this method, you can able to solve all problems from basic level to advanced level of questions asked based on Time and Distance in a faster approch.

Let's discuss the rules one by one with all Time and Distance related formulas with examples,

RULE 1 :

RULE 2 :

If a man travels different distances $d_1,d_2,d_3$,... and so on in different time $t_1,t_2,t_3$ respectively then,

RULE 3 :

If a man travels different distances $d_1,d_2,d_3$, and so on with different speeds $s_1,s_2,s_3$, respectively then,

RULE 4 :

If a distance is divided into n equal parts each travelled with different speeds, then,

where n = number of equal parts $s_1,s_2,s_3, ..., s_n$ are speeds.

RULE 5 :

If a bus travels from A to B with the speed x km/h and returns from B to A with the speed y km/h,then the average speed will be $({2xy}/{x + y})$

RULE 6 :

If $d_1$ distance is travelled in $t_1$ time and $d_2$ distance is travelled in $t_2$ time then,

Distance ∝ time [provided speed is constant]

RULE 7 :

If an object increases/decreases its speed from x km/hr to y km/hr. to cover a distance in $t_2$ hours in place of $t_1$ hours then [Here ($t_2 – t_1$) will be given].

RULE 8 :

If an object travels certain distance with the speed of $A/B$ of its original speed and reaches its destination 't' hours before or after, then the taken time by object travelling at original speed is

RULE 9 :

RULE 10 :

If a man travels at the speed of $s_1$, he reaches his destination $t_1$ late while he reaches $t_2$ before when he travels at $s_2$ speed, then the distance between the two places is

RULE 11 :

Time taken by 1st man to reach B after meeting 2nd man at C is '$t_1$' and time taken by 2nd man to reach A after meeting 1st man at C is '$t_2$' then:

RULE 12 :

If both objects run in opposite direction then, Relative speed = Sum of speeds.

If both objects run in the same direction then, Relative speed = Difference of Speeds.

RULE 13 :

Let a man take 't' hours to travel 'x' km. If he travels some distance on foot with the speed u km/h and remaining distance by cycle with the speed v km/h,then time taken to travel on foot.

Distance travelled on foot = Time × u

RULE 14 :

Formula to calculate the no. of rounds.

RULE 15 :

If any one overtakes or follows another,then time taken to catch

= $\text"distance between them"/\text"Relative speed"$

or meet =${(\text"Speed of 1st traveller") × \text"time"}/(\text"Differenc of speeds")$

RULE 16 :

Formula to calculate the no. of poles,

where n = No. of poles.

x = distance between consecutive two poles.

RULE 17 :

If in a certain time, '$d_1$' distance is travelled with '$s_1$' speed and $d_2$ distance is travelled with '$s_2$' speed then,

RULE 18 :

If a man covers $1/x$ part of Journey atu km/h,$1/y$ part at v km/h and $1/z$ part at w km/hr and so on, then his average speed for the whole journey will be $1/{1/{xu} + 1/{yv} + 1/{zw} +...}$

Refer: Get all Topic-wsie Quantitative aptitude problems for upcoming competitive exams