Shortcuts to Solve Time & Distance Questions in Govt. Job Exams

In this article we will share some Short Tricks on Speed, Distance & Time which are usually asked in all competitive exams. Before moving directly to the shortcuts, let us first understand the basics:

Speed is all about how fast or slow any object is moving. Speed is different from velocity (which involves direction). In Government exams, questions related to only speed are asked.

Speed is calculated as Distance/Time

A fast moving object will cover more distance and a slow moving object will cover less distance. Therefore, Distance is directly proportional to Speed.

Distance ∝ Speed or

• Distance/ Speed = constant = Time

• Distance = Speed * Time

Therefore the formula for Speed, Distance & Time is written as:

1. speed = distance/time

2. Formula of Distance: Distance = Speed * Time

Distance = Rate x Time

3. Time is given as

Formula of Time: time = distance/ speed

So Formula of time is distance upon speed

We use so many units to express distance. Sometimes in kilometers, sometimes in miles, sometimes in meters etc. Similarly is the case of time where we use seconds, minutes and hours. Speed is distance (given in units such as miles, feet, kilometers, meters, etc.) divided by time (hours, minutes, seconds, etc.). Therefore speed is written as a fraction that has distance units in the numerator and time units in the denominator, e.g., 25 miles/1 hour.

While attempting the questions, we should keep in mind the units given in the question. Generally used units of speed are kilometer per hour or simply kmph or (km/h) and meters per second or simple mps or (m/s)

To Convert km/h to m/sec use following formula

x km/hr=(x∗5/18) m/sec

and for converting m/s(meter per second) to k/hr (kilometer per hour) we use following formula

x m/sec= x *(18/5) km/h

Shortcut 1

When you cover a certain distance at the speed M and certain distance at speed N, then the average speed of the journey will be given by 2MN/(M+N)

Example : SRK reaches from his house Mannat to Filmcity by car the speed of 70km per hour and took an auto to come back from Filmcity which ran at the speed of 20km per hour. If the distance from Bandra to Filmcity was 5 km , find out the average speed of SRK from Bandra to Filmcity.

Solution: Here it is to be noted that if you are using the above shortcut, you won’t need the distance.

Using Shortcut 1, we get

• Average Speed = 2*70*20/(70+20)

• =2*70*20/90

• 31.11 km per hour

Now the above problem can be solved without using the shortcut also. Here’s how:

• The distance between Mannat and Filmcity is 5 kms

• Time taken to reach Filmcity = 5/70 =1/14

• Time taken to come back = 5/20 = ¼

• Total distance travelled = 5+5 = 10 kms

• Therefore, average speed = Total Distance Travelled/ Total Time Taken

• =10/(1/14+1/4)

• =10/(9/28)

• =280/9

• =31.11 km per hour

Now using this shortcut certainly saved a lot of your time.

Please note that this formula is applicable only when the distance between the two points is same. In case the distance is different, you will need to calculate the average speed using the formula:

Total Distance Travelled/ Total Time Taken.

Shortcut 2

When you travel from A to B with speed ‘x’ and reach early by time ‘t1’ and when you travel with speed ‘y’ and reach late by time ‘t2’, then the distance between A and B is given by xy(t1+t2)/(x-y)

Example : SRK goes to Filmcity from Mannat. If he goes by car at the speed of 70 kmph, he reaches 20 minutes early. If he goes by auto at the speed of 50 kmph, he reaches 40 minutes late. What is the distance between Filmcity and Mannat ?

Solution:

Using Shortcut 2, we get

• t1 = 20/60 =1/3

• t2=40/60=2/3

• t1+t2 =1/3+ 2/3 =1

• x = 70

• y = 50

• Therefore Distance = 70*50/20

• 175 kms

Now the above problem can be solved without using the shortcut also. Here’s how:

• Let the distance between Mannat and Filmcity is D kms

• Difference between the two times = 20 min+40 min

• =60 min

• = 1 hour

• Therefore,

• D/50-D/70 = 1

• 2D/350 = 1

• D = 175 kms

You just need to remember the formula in a way like:

(Product of speeds*sum of total time)/(Difference of speeds)

Please keep constant units while usingthe formulas

Shortcut 3

When two persons P1 and P2 travel from A to B having distance D between them with speed ‘a’ and ‘b’ such the P2 reaches B first and returns immediately and meets P1 at point C in between A and B, then

Distance travelled by P1 = 2aD/(a+b)

Distance travelled by P2 = 2bD(a+b)

Example : Varun and Ranveer decided to go to Delhi from Ambala which are 200 km apart. Varun travelled at the rate of 40 kmph and Ranveer travelled at 50 kmph. Reaching first, Ranveer immediately returned back to Delhi and met Varun at Mohri. Find the distance between Delhi and Mohri.

Solution:

Using Shortcut 3, we get

• D = 200 km

• a= 40kmph

• b= 50 kmph

• Therefore distance between Delhi and Mohri =

• 2*40*200/(40+50)

• 177.77 kms

While shortcuts save us a lot of time, please understand the applicability of shortcuts carefully. Also, while attempting the questions, one should keep in mind the units given in the question. Download Govt job News instant job notification & free study materials.

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