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Reasoning Skills

DIRECTION- II

shikha

January 15, 2016

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Direction-II includes degree-based puzzles. During schooling, Trigonometry was a main and interesting part of Maths in which angle based question were used to come.

Let’s recall the concept.

Starting with Zero degree

First Quadrant covers 90 Degree
Second Quadrant covers 180 Degree(Half of a circle or semicircle)
Third Quadrant covers 270 Degree(1/3 of complete circle)
Fourth Quadrant covers 360 Degree(Complete circle)

By default, we follow clockwise direction as we have seen above. But when we talk about Anticlockwise, the above diagram goes reverse.

An important fact related to directions is “Two Degree can only be computed, if they are in the same direction, whether Clockwise or Anticlockwise.” i.e. 45 Degree (Anticlockwise) – 30 Degree (Anticlockwise) = 15 Degree (Anticlockwise)

Take some puzzles based on this...

Problem1: A man is facing west. He turns 45 degrees in Clockwise and then another 180 degrees in the same direction and then 270 degrees in an anticlockwise direction. Which direction is he facing now?

Solution:

Step1: Add same directional degree first as 45+180 = 225 degrees (Clockwise)
Step2: Anticlockwise Direction is 270 degrees
Step3: Subtract Anticloclwise –Clockwise as 270-225= 45 degree
Step4: In the complete Journey, he goes 45 degrees extra in Anticlockwise direction
Step5: A man is facing west, by going 45 degrees in anticlockwise, he will face southwest as shown below:

Problem2:A man is facing North-west. He turns 90 degrees in the clockwise direction, then 135 degrees in the anticlockwise direction and which direction is he facing now?

Solution:

Step1: He turns clockwise 90 degrees and Anticlockwise 135 degrees. Subtract both as

135-90= 45 degree (Anticlockwise)
Step2: Man facing North West as

Step3: After 45 degrees turn, he stands straight in West Direction.

Problem3:A man is facing North-west. He turns 90 degrees in the clockwise direction, then 180 degrees in the anticlockwise direction and then another 90 degree in the same direction. Which direction is he facing now?

Solution:

Step1: First add the same directional degrees

180 + 90 =270 degrees (Anticlockwise)
Step2: Subtract Anticlockwise and Clockwise degrees
270-90= 180 degree (Anticlockwise)
Step3: A man facing North- west. When he move 180 degrees anticlockwise, he will reach in the fourth quadrant in South -East direction as shown below:

Problem4: I am facing east. I turn 100 degrees in the clockwise direction and then 145 degrees in the anticlockwise direction. Which direction am I facing now?

Solution:

Step1: Clockwise turn =100 degrees, Anticlockwise Turn = 145 degree. Subtract Both as

145-100 = 45 Degrees (Anticlockwise)
Step2: I am facing towards, by turning 45 degrees Anticlockwise, I am facing North-East direction now as shown:

Problem5: Karan walks positioning his back towards the sun. After some time, he turned left then right then towards the left again? In which direction is he going now?

Solution:

Step1: Two cases evolved here Sunrise and Sunset
Step2: During Sunrise, the Sun rises from the East. This way he is going to the South