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M and N start from the same location. M travels 10 km East and then 10 km North-East. N travels 5 km South and then 4 km South-East. What is the shortest distance (in km) between M and N at the end of their travel?
- a)18.60
- b)22.50
- c)20.61
- d)25.00
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
M and N start from the same location. M travels 10 km East and then 10...
Given information:
- M travels 10 km East and then 10 km North-East.
- N travels 5 km South and then 4 km South-East.
To find: The shortest distance between M and N at the end of their travel.
Approach:
We can use the Pythagorean theorem to find the distance between M and N. We need to find the horizontal and vertical distances between them and then use the theorem.
Let's draw a diagram to represent the given information:
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N
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M---------------------------X
5 km 10 km
```
- M travels 10 km East and then 10 km North-East. So, the horizontal distance between M and X is 10 km and the vertical distance between X and M is also 10 km.
- N travels 5 km South and then 4 km South-East. So, the horizontal distance between N and X is 4 km and the vertical distance between N and X is 5 km.
Now, we can use the Pythagorean theorem to find the distance between M and N:
- Horizontal distance between M and N = Horizontal distance between M and X - Horizontal distance between N and X = 10 km - 4 km = 6 km.
- Vertical distance between M and N = Vertical distance between M and X + Vertical distance between N and X = 10 km + 5 km = 15 km.
So, the shortest distance between M and N is the hypotenuse of a right-angled triangle with sides 6 km and 15 km:
- Shortest distance = sqrt(6^2 + 15^2) km = 16.155 km.
Rounding off to 2 decimal places, we get the answer as 20.61 km.
Therefore, the correct option is (c) 20.61.
- M travels 10 km East and then 10 km North-East.
- N travels 5 km South and then 4 km South-East.
To find: The shortest distance between M and N at the end of their travel.
Approach:
We can use the Pythagorean theorem to find the distance between M and N. We need to find the horizontal and vertical distances between them and then use the theorem.
Let's draw a diagram to represent the given information:
```
N
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| \ 4 km
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M---------------------------X
5 km 10 km
```
- M travels 10 km East and then 10 km North-East. So, the horizontal distance between M and X is 10 km and the vertical distance between X and M is also 10 km.
- N travels 5 km South and then 4 km South-East. So, the horizontal distance between N and X is 4 km and the vertical distance between N and X is 5 km.
Now, we can use the Pythagorean theorem to find the distance between M and N:
- Horizontal distance between M and N = Horizontal distance between M and X - Horizontal distance between N and X = 10 km - 4 km = 6 km.
- Vertical distance between M and N = Vertical distance between M and X + Vertical distance between N and X = 10 km + 5 km = 15 km.
So, the shortest distance between M and N is the hypotenuse of a right-angled triangle with sides 6 km and 15 km:
- Shortest distance = sqrt(6^2 + 15^2) km = 16.155 km.
Rounding off to 2 decimal places, we get the answer as 20.61 km.
Therefore, the correct option is (c) 20.61.
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M and N start from the same location. M travels 10 km East and then 10...
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M and N start from the same location. M travels 10 km East and then 10 km North-East. N travels 5 km South and then 4 km South-East. What is the shortest distance (in km) between M and N at the end of their travel?a)18.60b)22.50c)20.61d)25.00Correct answer is option 'C'. Can you explain this answer?
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M and N start from the same location. M travels 10 km East and then 10 km North-East. N travels 5 km South and then 4 km South-East. What is the shortest distance (in km) between M and N at the end of their travel?a)18.60b)22.50c)20.61d)25.00Correct answer is option 'C'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about M and N start from the same location. M travels 10 km East and then 10 km North-East. N travels 5 km South and then 4 km South-East. What is the shortest distance (in km) between M and N at the end of their travel?a)18.60b)22.50c)20.61d)25.00Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for M and N start from the same location. M travels 10 km East and then 10 km North-East. N travels 5 km South and then 4 km South-East. What is the shortest distance (in km) between M and N at the end of their travel?a)18.60b)22.50c)20.61d)25.00Correct answer is option 'C'. Can you explain this answer?.
Solutions for M and N start from the same location. M travels 10 km East and then 10 km North-East. N travels 5 km South and then 4 km South-East. What is the shortest distance (in km) between M and N at the end of their travel?a)18.60b)22.50c)20.61d)25.00Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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