Direction & Distance Tricks & Tips
This article covers the topic of Direction and Distance. The questions of which are asked under the reasoning section in various competitive exams like IBPS Clerk, SBI Clerk, SSC CGL, Placement Aptitude, IBPS PO, SBI PO, NICL AO, LIC AAO, SBI Associate Clerk, SBI Associate PO, CAT and others. The key factor to solve this type of questions are have your basics right. So be strong in the basics first because knowing the conventional method gives you an upper hand when you lost track of the shortcut method. After you have acquired the basics and have gone to a pro, try to learn the tricks of various shortcuts.
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Learning the shortcuts and tricks will help you to solve the problems faster in a way that it provides you with additional time to solve other questions. Direction and Distance topic is one of the easiest topic in the reasoning section and you can score full marks with great accuracy if you learn the nuances of this topics. This is a definite topic in the exams , so there is no confusion if it will come in the exam or not.
In this article, we are going to discuss how to solve direction sense questions along with the shortcuts and tricks to solve the question in less than a minute. First make a sketch of the data that is provided to solve the direction test. We have described the direction and distance test along with shortcuts , tips and tricks. So learn these tricks and shortcuts to arrive at the answer with great accuracy and speed.
- Basic Directions
- Pythagoras theorem
1. Basic Directions: We have 8 basic directions which should be crystal clear to us for attempting distance and direction questions.
One key point that should be kept in mind is that If not mentioned we always assume that the person is facing north.
2. Pythagoras theorem: According to this theorem,” The square of Hypotenuse is always equal to the sum of the squares of the other two sides of the right angle triangle”.
Suppose we have a triangle having base p, height q and hypotenuse r. Then according to this theorem:
p^{2}+q^{2}=r^{2}
Now you have the basics required to atttempt Distance & Direction questions. So let us try to look at few questions on the same so that you will get to know the proper approach to solve these questions.
Some other basics:
1.B is to the east of A.
2. B is to the west of A.
3. B is to the north of A.
4. B is to the south of A.
5. B is to the North East of A.
6. B is to the North West of A.
7. B is to the South East of A.
8. B is to the South West of A.
Direction: Ashok started walking towards South. After walking 50 meters he took a right turn and walked 30 meters. He then took a right turn and walked 100 meters. He then took a left turn and walked 30 meters and stopped. How far and in which direction was he from the starting point?
Solution:
Ashok started walking towards south.
After walking 50 meters…
..he took a right turn…
Some people have doubt in deciding left or right in direction questions; they can replace right by clockwise and left by anticlockwise. So now moving right (clockwise) from the tip of the arrow.
…and walked 30 meters.
He took a right turn…
…and walked 100 meters.
He took a left turn…
…and walked 30 meters.
Now for finding how far he has moved, we will check two things:
- Horizontal displacement
- Vertical displacement
Horizontal displacement = 30+30 = 60m
Vertical displacement = 100-50 = 50m
Final displacement = √(60^{2}+50^{2}) = √(3600+2500) = √6100 = 10√61 m
Now for finding the direction with reference to initial position, we will draw a line joining two points which will give us the direction.
We can clearly see that the direction in which Ashok moved is northwest.
So the final answer for this question will be “Ashok moved 10√61 meters in northwest direction”.
Directions: Jay starts his van from point X and covers a distance of 10 km towards west, then he turns north and covers a distance of 7 km. Again, he takes a right turn and covers 25 km. Now he covers 6 km, after taking a left turn. At last he takes a left turn and covers 15 km and stops at point Z.
Solution:
Jay starts his van from point X and covers a distance of 10 km towards west
then he turns north
and covers a distance of 7 km
Again, he takes a right turn
…and covers 25 km
Now he covers 6 km, after taking a left turn.
At last he takes a left turn…
…and covers 15 km and stops at point Z.
Q. Towards which direction was the van running before stopping at point Z?
- North
- East
- West
- South
- None of these
Solution: We can clearly see that van was running towards west before stopping at point Z.
So the correct answer is C.
Q. How far is Jay from point X?
- 23 km
- 25 km
- 17 km
- 50 km
- None of these
Soution:
Horizontal movement = 10-25+15 = 0 kms
Vertical movement = 7+6 = 13 km
So final movement = = √(0^{2}+13^{2}) = √169 = 13 km
Direction of movement is North.
Key points related to Distance & Direction:
- Always remember the basic directions.
- Pythagoras theorem is valid only for a right angle triangle.
- Always approach the question step by step.
- In the End, join the initial and final point to get to know the distance and relative direction.
- If in any of the questions, the relative direction is given.i.e. P is to the north of Q, then you can use the basic directions to get the location of P and Q.
Example 1: A man goes 3 kms. East from point A and then takes a right turn from point B to move 4 kms. to point C. What is the minimum distance between point A and point C?
Solution: In order to find the minimum distance between these points, we use a little bit of geometry. We know that the minimum distance between these points will lie along the hypotenuse of the right-angled triangle formed by these points
Now applying Pythagoras theorem, the distance between the starting point A and final point C is 5 kms i.e. the square root of the sum of squares of 3 and 4.
Now, in case the question was: “In which direction is the starting point with respect to C”; the answer would be North-west.
Another question could be: “In which direction is he walking towards point C”; the answer would be South.
While calculating the distance from a starting point to the destination point when the points form a right angled triangle, the prior knowledge of Pythagorean Triplets (3-4-5, 5-12-13, 8-15-17 etc.) is generally very helpful in calculating the distances involved as it saves time spent on calculations. Let us solve an example that uses this knowledge.
Example 2: A child is looking for his father. He went 90 metres in the East before turning to his right. He went 20 meters before turning to his right again to look for his father at his uncle’s place 30 metres from this point. His father was not there. From here he went 100 metres to the North before meeting his father in a street. What is the smallest distance between the starting point and his father’s position?
Solution:
Clearly, the child meets his father at E.
Now, AF = (AB – FB)
= (AB – DC) = (90 – 30) m = 60 m.
EF = (DE – DF) = (DE – BC)
= (100 – 20) m = 80 m.
Now the distance is square root of (60^{2} + 80^{2}), which will be 100 metres.
We can clearly see from the above example that knowledge of basic concepts can go a long way in reducing the time you take to solve problems, along with improving your accuracy. Make sure you place sufficient emphasis on the topics such as ‘direction based questions’, and your performance is surely meant to improve.
Example 1: Aarthi walked 4 km west of her house and then turned south covering 3 km. Finally, She moved 5 km towards east. In which direction she is now with respect to starting point?
Solution: From the above diagram, we can find that she is South East to her starting point.
Example 2: Sandhya starting from her house, goes 4 km in the East, then she turns to her right and goes 3 km. What is the shortest distance to reach her house?
Solution:
In order to find the minimum distance between these points. We know that the shortest distance between these points will lie along the hypotenuse of the right-angled triangle formed by these points
Now applying Pythagoras theorem, the distance between the starting point A and final point C is 5 kms i.e. the square root of the sum of squares of 3 and 4.
Other Possible Questions
An important point to learn from this question could be the fact that you might be asked to specify the direction of the specific point, for example, the question might state: “in which direction is she with respect to the starting point”. The answer would be South-east.
Now, in case the question was: “In which direction is the starting point with respect to C”; the answer would be North-west.
Another question could be: “In which direction is he walking towards point C”; the answer would be South.
IMPORTANT POINTS TO REMEMBER WHILE SOLVING DISTANCE-DIRECTION QUESTION:
– To know thedirections on the plane of paper
– Tosketch out the directions as per the instructions in the question
– To remember that on thesurface of paper
- The direction ofright turnis always in theclockwise direction
- The direction ofleft turnis always in theanti-clockwise direction
- The direction ofNorthisupwards
- The direction ofSouthisdownwards
- The direction ofEastis‘to the right’
- The direction ofWestis‘to the left’
– To formulate a step by step analysis of directions and distances
– To find the final direction or the distance between the starting and final point or both
3 Tricks to Analyze and Calculate Direction and Distance
#1. THE EIGHT POINTED STAR
Consider all eight directions while solving the given question. Draw the different directions out as follows:
#2. WHERE ART THOU?
Always consider yourself as facing North. Solve the question accordingly. Now your left hand is to the West side and your right hand is to the East side.
#3. TWIST AND PLOT
For rotation based questions, rotate the person in clockwise or anticlockwise direction relative to the direction he/she was facing last as per the question. Suppose the person was last facing East and in the question, it is given that he turns 45° to his right. Then the rotation will be as shown below:
Note:Rotation to the right is clockwise rotation & rotation to the left is anticlockwise rotation when looking down at the paper. This is irrespective of the direction in which you are facing.
So now the person is facing South-East.
EXAMPLE:
Let us illustrate all this things with an example.
Mohan started from his home and started walking East. After walking a distance of 5 km, he turned to the right and walked 3km. He then again turned to the right and walked 5 km. After this he turned 30° to his right and covers 6 km. In which direction is he and how far is he from his house?
Let us first draw directions as shown
STEP 1: Mohan started from his home and started walking towards East. That means Mohan is facing East.
STEP 2: After walking a distance of 5km, he turned to the right and walked 3km.
This tell us that he first walked 5 km towards East and turns right (now he is facing South) and then walks 3km in this direction (i.e. towards South).
STEP 3: Then he turns to the right and walks 5 km. That means he turns towards West and walks 5 km towards West.
STEP 4: Now he turns 30° to his right and walks 6 km. This is the point where one makes a mistake. We know that Mohan is now facing West and he has to turn 30° from West towards North. Hence now he is facing North-West. So he walks 6 km towards North-West. Thus his final position is as shown below.
So Mohan is towards West from his house. To find out the distance between Mohan and his house we will apply Pythagoras theorem.
AD = 3 km, ED = 6 km
AE = √ (ED^{2} – AD^{2} ) = √ (6^{2} – 3^{2})
AE = √ (36-9) = √ (27)
Therefore AE = 3√3
Hence Mohan is 3√3 kms West from his house.
[Note: 30° 60° 90° theorem is applied in this problem where ∠ A = 90°, ∠ B = 60° and ∠ E = 30°
In 30° 60° 90° theorem, the smallest side is x, the larger side is √3 x and hypotenuse is 2x. So this problem is pretty easy to solve. It doesn’t require too many calculations.]
Practice Problems On Direction & Distance
(1) 2 km.
(3) 6 km.
(4) 8 km.
- From a point, Sahil starts walking in east direction. After walking for 15 m he takes a right turn. Now he walks for 12 m before turning to his right again. Next he walks 5 m and again turns in same direction as before. He now walks for 20 m before stopping at a point. How far is this point from the point where Sahil started?
A) 4 √10 m
B) 3 √22 m
C) 7 m
D) 2√41 m
E) 12 m - Abhi and Asha start cycle race from point A. They both start in east direction. After cycling for 7 m, Abhi continues straight while Asha takes a left turn. They both cycle for 6 m before turning right and left directions respectively. Next
(1) Asha cycles for 8 m and takes a right turn. Now she cycles for 5 m before turning to right again.
(2) Abhi cycles for 4 m and takes a left turn. Now he cycles for 6m before turning to left again.
If both stop at these points, how much respective distance they have to travel to meet each other on their current paths?
A) 10 m, 15 m
B) 13 m, 17 m
C) 15 m, 20 m
D) 18 m, 24 m
E) Cannot be determined - From point A, Swati started walking in south direction. She walked for 4 m and took a right turn. Next she walked 5 m and turned to her left. Next she walked for 3 m and turned to her right. Next she walked 4 m and turned to her right again. Next she walked 15 m and turned to her right again and stopped at point B after walking 7 m. Find distance AB.
A) 2√22 m
B) 3√21 m
C) 2√19 m
D) 4√17 m
E) None of these - Point P is 10 m west of point Q. Point R is 4 m north of point P. Point T is 3 m east of point S and point S is 5 m south of point Q. What is the direction of point R with respect to point T?
A) South-east
B) South
C) North-east
D) North-west
E) West - Anaya started from a point in some direction. After walking for some time, she turned to her right and continued walking. Now walking for some distance she turned to her left and after this finally to her right. If now she is walking in west direction, in which direction did she started her journey?
A) North
B) West
C) East
D) South
E) East or west - Sheetal started from point in South direction. After walking for 5 km she took a right turn. Now she walked another 5 km and took a left turn. Then after walking for 2 km she took a right turn. After covering more 2 km she turned 45^{o} in clockwise direction. She is facing which direction now?
A) South West
B) South East
C) North East
D) North West
E) None of these
Directions (7-8): Point P is 5 m south of point A. Point T is 8 m east of point Q. Point Z is 4 m west of point V. Point P is 6 m west of point B. Point V is 6 m south of point T. Point Q is 4 m south of point B.
- Find distance AZ.
A) 5√13 m
B) 6√13 m
C) 4√14 m
D) 7√15 m
E) 3√11 m - A person starts from point B in north direction. Walks for 6 m and reaches point C, takes a right turn walks for 5 m reaches point F. Again he takes a right turn, walks for 3 m, reaches point H, now takes a left turn, reaches point K, now takes a final right turn to reach point T. Find the area enclosed by points B, Q, T, K, H, F and C.
A) 58m^{2}
B) 65m^{2}
C) 71m^{2}
D) 76m^{2}
E) None of these
Directions (9-10): Point A is 8 m west of point B. Point E is 2 m east of point F. Point G is 3 m east of point H. Point E is 3 m north of point of point D. Point C is 9 m west of point D. Point G is 9 m north of point F. Point C is 6 m south of point B.
- Find distance AH.
A) 7√6 m
B) 7√5 m
C) 6√6 m
D) 6√5 m
E) None of these - A person starts from point G in east direction. Walks for 6 m, takes a right turn, now walks for 5 m. Now he takes a left turn, walks for 3 m, then after two consecutive right turns he reaches point E. Find the distance travelled by him to reach point E.
A) 27 m
B) 25 m
C) 23 m
D) 24 m
E) 28 m
Directions (1-5): Study the following information carefully and answer the questions that follow.
A country has the following types of traffic signals.
3 green lights = go at 60 kmph speed
2 green lights = go at 40 kmph speed
1 green light = go at 20 kmph speed
3 red lights = stop
2 red lights = turn left
1 red light = turn right
A person starts driving from a point in West direction and he encounters the following traffic signals:
Starting point – 1 green light;
After 15 minutes, 1st signal – 2 red & 2 green lights;
After 24 minutes, 2nd signal – 1 red & 3 green lights;
After 45 minutes, 3rd signal – 1 red & 2 green lights;
After 18 minutes, 4th signal – 3 red lights;
- Find the total distance he covered up to the last signal.
A) 76 km
B) 78 km
C) 70 km
D) 75 km
E) 79 km - After passing the third signal if the person encounters fourth signal after half an hour, then what is his final position with respect to the starting point?
A) 4 km to the south and 50 km to the east
B) 55 km directly to the north-west
C) 4 km to the north and 50 km to the west
D) 4 km to the north and 45 km to the west
E) None of these - If instead of starting in West direction, the man starts in South direction, then what is his position with respect to the starting point?
A) 50 km to the south and 4 km to the west
B) 54 km directly to the north-west
C) 50 km to the north and 4 km to the west
D) 50 km to the south and 4 km to the east
E) None of these - If after the first signal,
2nd signal: 2 red and 2 green lights, and
3rd signal: 1 red and 3 green lights, then what is the distance covered up to the last signal?
A) 69 km
B) 60 km
C) 68 km
D) 67 km
E) 65 km - If the person stops at 3rd signal, then what is his final position with respect to his starting position?
A) 50 km to the north-west
B) 52.5 km to the south-west
C) 52.5 km to the north-east
D) 50.5 km to the south-west
E) 50.5 km to the south-east
Directions (6-8): Point D is 2 km to the north of point C. Point G is 8 km to the north of point H. Point A is 15 km to the south of point B. Point C is 8 km to the east of point B. Point E is 10 km to the north of point F which is 4 km to the west of point G. Point D is 4 km to the west of point E.
- Find shortest distance BH.
A) 16√4 km
B) 32 km
C) 15 km
D) 16√2 km
E) None of these - If a person after taking 2 turns reaches to point B from point F via point A, then what is the distance that he covered?
A) 32 km
B) 34 km
C) 30 km
D) 35 km
E) 36 km - If a person starts from point H and reaches point S which is south of point C, then find distance CS + HS – EF.
A) 12 km
B) 13 km
C) 15 km
D) 14 km
E) None of these - Priya started from point A. after walking for some time, she turned to her right and continued walked, then after some time turned to her right again. Now walking for some distance she turned to her left and after this finally to her right. If now she is walking in west direction, in which direction did she started her journey from point A?
A) West
B) East
C) South
D) North
E) Cannot be determined - Tiya started from her home to office. She started in east direction. After walking for 4 km she turned to her left and walked 8 km, now she turned left and walked 2 km. After this she turned to right walked 4 km. Now after turning to her right she walked 13 km and reached office. Find the shortest distance between her office and home.
A) 3√43 m
B) 3√41 km
C) 4√41 m
D) 5√38 m
E) None of these
Direction: Q(1-5) There are 5 friends A, B, C, D and E standing randomly. B is to the northeast of E. D is 2km to the east of E, who is 6km to the west of A. C is to the northwest of D and in the line of EB. D is 4km the south of B.
- In which direction is C with respect to A ?
A.South west
B.South east
C.Northeast
D.Northwest
E.None of these - In which direction is A with respect to B ?
A.Southeast
B.Southwest
C.Northwest
D.Northeast
E.None of these - What is the distance between D and A ?
A.5km
B.4km
C.6km
D.3km
E.None of these - What is the shortest distance between B and A?
A.5√7km
B.4√2km
C.6√2km
D.3√5km
E.None of these - What is the shortest distance between between B and E?
A.2√7km
B.5 √2km
C.7√2km
D.2√5km
E.None of these
Directions : Q(6-7) – Bala walked 25km towards west, took a left turn and walked 15km. He again took a left turn and walked 30km. He then took a right turn and stopped.
- Now he was facing which direction ?
A.West
B.East
C.South
D.North
E.None of these - Instead of turning right at the end if he took left and walked 20km, what is the shortest distance to his starting point?
A.3√7km
B.2√5km
C.7√2km
D.5√2 km
E.None of these - Raghav starts walking in south direction and walks a distance of 7 meters. Now he tooks a left turn and walk 6m. Again he takes a left turn and walk 15m and reached a point P. Find the distance between starting point and P and in which direction is the person from the initial point.
A.10m, south east
B.10m, north east
C.20m, north west
D.20m, south west
E.None of these - Dheepthi started from point A in south direction. After walking for 4 m she turned to her right and walked 5 m. Now she turned to her left and walked 3 m after which she turned to her right. Now she walked 4 m and turned to her right again and walked 15 m. Now finally she turned to her right and after walking for 7 m, she stopped at point B. What is the distance AB?
A.2√34 m
B.34 m
C.3√17 m
D.2√17 m
E.None of these - Riya started from her home to office. She started in east direction. After walking for 4 m she turned to her left and walked 8 m, now she turned left and walked 2 m. After this she turned to right walked 4 m. Now after turning to her right she walked 13 m and reached office. Find the shortest distance between her office and home.
A.87 m
B.9√41 m
C.26 m
D.3√41 m
E.None of these
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