Question:
Sakshi starts from her college and walks 12 km towards the North. She then turns right and walks 5 km. After that, she turns right again and walks 4 km. She then turns left and walks 7 km. Finally, she turns left and walks 1 km. How far is Sakshi from her college and in which direction?
Sakshi starts from her college and walks 12 km towards the North. She then turns right and walks 5 km. After that, she turns right again and walks 4 km. She then turns left and walks 7 km. Finally, she turns left and walks 1 km. How far is Sakshi from her college and in which direction?
Show Hint
Always verify the final square root before selecting the option.
Here,
\[
9^2+12^2=81+144=225
\]
and
\[
\sqrt{225}=15,
\]
not 13. Also, \((9,12,15)\) is a multiple of the famous Pythagorean triplet \((3,4,5)\).
Hence, the correct option is (D) 15 km, North-East.
Updated On: Jun 30, 2026
- 13 km, North-East
- 12 km, South-East
- 10 km, North-West
- 15 km, North-East
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Concept:
In direction problems, calculate the net displacement separately along the North--South and East--West directions.
• Movement towards North is taken as positive and South as negative.
• Movement towards East is taken as positive and West as negative.
• The shortest distance from the starting point is obtained using the Pythagoras Theorem: \[ \text{Distance}=\sqrt{(\text{Vertical Displacement})^2+(\text{Horizontal Displacement})^2}. \]
Step 1: Trace Sakshi's complete movement.
\[ \begin{array}{|c|c|c|} \hline \textbf{Movement} & \textbf{Distance} & \textbf{Direction} \\ \hline 1 & 12\ \text{km} & \text{North} \\ \hline 2 & 5\ \text{km} & \text{East} \\ \hline 3 & 4\ \text{km} & \text{South} \\ \hline 4 & 7\ \text{km} & \text{East} \\ \hline 5 & 1\ \text{km} & \text{North} \\ \hline \end{array} \]
Step 2: Calculate the net displacement in North--South direction.
\[ 12-4+1=9\ \text{km North} \] Hence, \[ \boxed{\text{Net Vertical Displacement}=9\ \text{km North}} \]
Step 3: Calculate the net displacement in East--West direction.
\[ 5+7=12\ \text{km East} \] Hence, \[ \boxed{\text{Net Horizontal Displacement}=12\ \text{km East}} \]
Step 4: Find the shortest distance from the college.
Using Pythagoras Theorem, \[ \begin{aligned} \text{Distance} &=\sqrt{9^2+12^2} \\ &=\sqrt{81+144} \\ &=\sqrt{225} \\ &=15\ \text{km}. \end{aligned} \] Since the final position lies towards the North and the East of the starting point, the direction is
North-East. Therefore, \[ \boxed{\text{Required Answer}=15\ \text{km, North-East}} \]
• Movement towards North is taken as positive and South as negative.
• Movement towards East is taken as positive and West as negative.
• The shortest distance from the starting point is obtained using the Pythagoras Theorem: \[ \text{Distance}=\sqrt{(\text{Vertical Displacement})^2+(\text{Horizontal Displacement})^2}. \]
Step 1: Trace Sakshi's complete movement.
\[ \begin{array}{|c|c|c|} \hline \textbf{Movement} & \textbf{Distance} & \textbf{Direction} \\ \hline 1 & 12\ \text{km} & \text{North} \\ \hline 2 & 5\ \text{km} & \text{East} \\ \hline 3 & 4\ \text{km} & \text{South} \\ \hline 4 & 7\ \text{km} & \text{East} \\ \hline 5 & 1\ \text{km} & \text{North} \\ \hline \end{array} \]
Step 2: Calculate the net displacement in North--South direction.
\[ 12-4+1=9\ \text{km North} \] Hence, \[ \boxed{\text{Net Vertical Displacement}=9\ \text{km North}} \]
Step 3: Calculate the net displacement in East--West direction.
\[ 5+7=12\ \text{km East} \] Hence, \[ \boxed{\text{Net Horizontal Displacement}=12\ \text{km East}} \]
Step 4: Find the shortest distance from the college.
Using Pythagoras Theorem, \[ \begin{aligned} \text{Distance} &=\sqrt{9^2+12^2} \\ &=\sqrt{81+144} \\ &=\sqrt{225} \\ &=15\ \text{km}. \end{aligned} \] Since the final position lies towards the North and the East of the starting point, the direction is
North-East. Therefore, \[ \boxed{\text{Required Answer}=15\ \text{km, North-East}} \]
Was this answer helpful?
0
0
Top PU LLB Logical Reasoning Questions
- Fact 1: All dogs like to run
Fact 2: Some dogs like to swim
Fact 3: Some dogs look like their masters
If the first three statements are facts, which of the following statement must also be a fact?
i) All dogs who like to swim look like their masters
ii) Dogs who like to swim also like to run
iii) Dogs who like to run do not look like their masters - Pointing to Kavish, Shilpa said- His mother's brother is the father of my son Akash, How is Kavish related to Shilpa?
- A policeman left his police post and proceeded south $4\text{ km}$ on hearing a loud sound from point A. On reaching the place, he heard another sound and proceeded $4\text{ km}$ to his left to the point B. From B he proceeded left to reach another place C, $4\text{ km}$ away. In which direction he has to go to reach his police post?
- Some people decided to go to a movie and spend Rs. 192 on the snacks. While going for a movie, they found that 4 people had not shown up. Therefore, the amount to be spent on snacks was recalculated, and an extra burden of Rs. 8 per person was imposed on the friends present. How many friends had planned to go to the movie initially?
- Pointing to a photograph, Mrs. Riya said, “He is the son of the only daughter of my grandfather’s only son.” How is the boy in the photograph related to Mrs. Riya?
View More Questions
Top PU LLB Direction sense Questions
Top PU LLB Questions
- Which one of the following is not a theme of the government initiative Azadi Ka Amrit Mahotsav?
- Mithali Raj recently became the first female cricketer to win which of the following awards?
- Which institution released the report titled 'Tobacco: Poisoning Our Planet'?
- Operation 'Rakth Chandan' was associated with which institution?
- Which Indian state is the first to conduct statewide Lok Adalat through video conferencing?
View More Questions