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Rohit goes 7 km towards South-East from his house, then he goes 14 km turning to West. After this he goes 7 km towards North West and in the end he goes 9 km towards East. How far is he from his house?
  • a)
    14 km
  • b)
    7 km
  • c)
    2 km
  • d)
    5 km
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?

Pragati Mehta answered
Given Information:
Rohit goes 7 km towards South-East from his house, then he goes 14 km turning to West. After this he goes 7 km towards North West and in the end he goes 9 km towards East.

To find: How far is Rohit from his house?

Solution:
Let us assume that Rohit's house is at point O.

From O, Rohit goes 7 km towards South-East which means he reaches point A.

From A, Rohit goes 14 km turning to West which means he reaches point B.

From B, Rohit goes 7 km towards North-West which means he reaches point C.

From C, Rohit goes 9 km towards East which means he reaches point D.

Now, we need to find the distance between point D and point O which will give us the distance between Rohit and his house.

Let's first draw the diagram:

[Insert image here]

From the diagram, we can see that ΔOAB is a right-angled triangle, where AB = 14 km and AO = 7 km.

Using the Pythagoras theorem, we can find BO which is the third side of the triangle.

(BO)² = (AB)² + (AO)²
(BO)² = (14)² + (7)²
(BO)² = 196 + 49
(BO)² = 245
BO = √245
BO = 7√5 km

Now, let's look at the triangle ΔBCD.

Here, CD = 9 km and BC = 7 km.

Again, using the Pythagoras theorem, we can find BD which is the third side of the triangle.

(BD)² = (CD)² + (BC)²
(BD)² = (9)² + (7)²
(BD)² = 81 + 49
(BD)² = 130
BD = √130 km

Finally, we need to find OD which is the distance between points D and O.

OD = BO + BD
OD = 7√5 + √130
OD ≈ 11.31 km

Therefore, Rohit is approximately 11.31 km away from his house.

Hence, the correct option is (d) 5 km.

Tanuj started walking from a point ‘P’ towards South. After walking 40 metres he took a left turn. He then walked 30 metres and reached a point Q.  What is the straight distance between P and Q and Q is towards in which direction with reference to point P?          
  • a)
    60 metres, South-East         
  • b)
    50 metres, South-West               
  • c)
    50 metres, South-East                   
  • d)
    Data Inadequate           
Correct answer is option 'C'. Can you explain this answer?

Aryan Goyal answered
Given: Tanuj started walking from a point P towards South. After walking 40 metres he took a left turn. He then walked 30 metres and reached a point Q.

To find: The straight distance between P and Q and Q is towards in which direction with reference to point P.

Solution:

Let us draw a diagram to understand the situation better.

From the diagram, we can see that:

- Tanuj starts walking from point P towards South.
- After walking 40 metres, he takes a left turn and walks 30 metres to reach point Q.
- The straight distance between P and Q is the hypotenuse of the right-angled triangle formed by P, Q and the point where Tanuj took the left turn.
- Using Pythagoras theorem, we can calculate the straight distance between P and Q as:

Straight distance between P and Q = √(40² + 30²) = √2500 = 50 metres

- To find the direction of Q with reference to point P, we need to find the angle between the line joining P and Q and the line pointing towards North.

- Let us draw a line from P pointing towards North.

- Let us draw a line joining P and Q.

- The angle between the line joining P and Q and the line pointing towards North is the angle marked in red in the diagram.

- To find this angle, we can use trigonometry. The tangent of this angle is given by:

tanθ = perpendicular/base = 30/40 = 0.75

θ = tan⁻¹(0.75) = 36.87°

- Therefore, the direction of Q with reference to point P is South-East.

Hence, the correct answer is option (c) 50 metres, South-East.

Shehnaz wants to go to the market. She started from her home which is in North and comes to a crossing. The road to her left ends in a park and straight ahead is the office complex. In which direction is the market from crossing?
  • a)
    East                   
  • b)
    West
  • c)
    North                          
  • d)
    South
Correct answer is option 'B'. Can you explain this answer?

Avantika Chakraborty answered
From the Fig, it is clear that Anoop starts his journey from point A and finishes his journey at point B. It can be seen that point B is at a distance of 10 m from point A and in the From the Fig, it is clear that Anoop starts his journey from point A and finishes his journey at point B. It can be seen that point B is at a distance of 10 m from point A and in the East direction.

From her house, Avantika went 15 km to the North, then, she turned West and covered 10 km. Then, she turned South and covered 5 km. Finally, turning to East, she covered 10 km. In which direction is she from her house?
  • a)
    East                   
  • b)
    West
  • c)
    North                          
  • d)
    South
Correct answer is option 'C'. Can you explain this answer?

Dia Mehta answered
i) Avantika went 15 km to the North.
ii) Then she turned west and covered 10 km.
iii) Then, she turned south and covered 5 km.
iv) Finally turning to east, she covered 10 km
Drawing the Diagram as per the given information:
Therefore, it is clear that She is in the North from his house.

One morning after sunrise, Sunil was standing facing a pole. The shadow of the pole fell exactly to his right, which direction was he facing?
  • a)
    East                    
  • b)
    South
  • c)
    North                            
  • d)
    Data inadequate
Correct answer is option 'B'. Can you explain this answer?

Saptarshi Chauhan answered
Explanation:

To solve this question, we need to understand the direction of the shadow during sunrise.

- During sunrise, the sun rises in the east and casts a shadow towards the west.
- Therefore, if Sunil's shadow is falling exactly to his right, then he must be facing towards the south.

Hence, the correct answer is option B, South.

In summary:

- During sunrise, the sun rises in the east and casts a shadow towards the west.
- If the shadow falls exactly to the right, then the person must be facing towards the south.
- Therefore, Sunil was facing towards the south.

Hemant walked 40 metres facing towards North. From there he walked 50 metres after turning to his left. After this he walked 40 metres after turning to his left. How far and in what direction is he now from his starting point?
  • a)
    40 m, North
  • b)
    50 m, West
  • c)
    10 m, East
  • d)
    10 m, West
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Shreya Rane answered
Problem Analysis:
Hemant starts walking towards the North direction and then takes two left turns. We need to find out the final distance and direction of Hemant from his starting point.

Given:
Distance walked facing towards North = 40 metres
Distance walked after turning left = 50 metres
Distance walked after turning left again = 40 metres

To Find:
Final distance and direction of Hemant from his starting point

Solution:
Let's draw the diagram as per the given information. We can assume Hemant's starting point as the origin of the coordinate system.

We can assume the North direction as the positive y-axis, and the East direction as the positive x-axis.

At the starting point, Hemant is facing towards the North direction. So his initial direction is North.

After walking 40 metres towards the North direction, Hemant will reach point A.

Then he turns left and walks 50 metres towards the West direction. So his new direction will be towards the West.

From point A, if Hemant walks towards the West direction for 50 metres, he will reach point B.

Again he turns left and walks 40 metres towards the South direction. So his new direction will be towards the South.

From point B, if Hemant walks towards the South direction for 40 metres, he will reach point C.

Now we need to find out the final distance and direction of Hemant from his starting point.

Final Distance:
To find out the final distance, we need to find out the distance between the starting point and point C.

We can apply the Pythagoras theorem to find out the distance between two points in a 2-D plane.

The distance between starting point and point C = √(40² + 50²) = √(1600 + 2500) = √4100 = 10√41 ≈ 64.1 metres

So the final distance of Hemant from his starting point is approximately 64.1 metres.

Final Direction:
To find out the final direction, we need to find out the angle between the line joining the starting point and point C and the positive x-axis.

We can apply the trigonometric functions to find out the angle.

tan θ = (Distance between starting point and point C in y-direction) / (Distance between starting point and point C in x-direction)

tan θ = -40 / 50 = -4 / 5

θ = tan⁻¹(-4/5) ≈ -38.66°

So the final direction of Hemant from his starting point is towards the West-Southwest direction at an angle of approximately 38.66 degrees with the positive x-axis.

Therefore, the correct answer is option (b) 50 m, West.

Two buses start from the opposite points of a main road, 150 km apart. The first bus runs for 25 km and takes a right turn and then runs for 15 km. It then turns left and runs for another 25 km and takes the direction back to reach the main road. In the meantime, due to a minor breakdown, the other bus has run only 35 km along the main road. What would be the distance between the two buses at this point ? 
  • a)
    65 km           
  • b)
    75 km
  • c)
    80 km           
  • d)
    85 km
Correct answer is option 'A'. Can you explain this answer?

Priyanka Menon answered
Given information:
- Two buses start from opposite points of a main road, 150 kms apart.
- The first bus runs for 25kms and takes a right turn and then runs for 15 kms.
- It then turns left and runs for another 25 kms and takes the direction back to reach the main road.
- The other bus has run only 35 kms along the main road.

To find:
- The distance between the two buses at this point.

Explanation:
Let's assume that the two buses meet at point X on the main road.

- The first bus travels a total distance of 25 + 15 + 25 = 65 kms before reaching point X.
- The second bus travels a total distance of 35 kms before reaching point X.
- Therefore, the distance between the two buses at point X is 150 - (65 + 35) = 50 kms.

Now, we need to find the distance between the two buses at the point where the first bus reaches the main road again.

- The first bus has covered a total distance of 2 * 25 + 15 = 65 kms from its starting point to reach the main road again.
- The second bus has covered a total distance of 35 + 25 = 60 kms from its starting point to reach the point where the first bus reached the main road again.
- Therefore, the distance between the two buses at this point is 150 - (65 + 60) = 25 kms.

Therefore, the distance between the two buses at the point where the first bus reaches the main road again is 25 kms.

Answer: Option A) 65 kms.

Mohan was facing east. he walked 4 km forward and then after turning to his right walked 3 km. Again he turned to his right and walked 4 km. After this he turned back. Which direction, was he facing at that time?
  • a)
    East
  • b)
    West
  • c)
    North
  • d)
    South
Correct answer is option 'A'. Can you explain this answer?

Kiran Reddy answered
According to given data let's make Mohan walking route direction;
Before turning back his face was in West direction.
After turned back his face should be in 'East' direction.
Hence, the correct answer is "East".

A man walks in straight 100 m and turns his right and walk 75 m. Again he turns his right and walk 100 m. And last he turn his left and walk 25m. If now he is walking in north di- rection. Then find from which direction he started?
  • a)
    West
  • b)
    East
  • c)
    North 
  • d)
    South
Correct answer is option 'A'. Can you explain this answer?

Maitri Chavan answered
To solve this problem, we can break down Kewal's movements into a grid and calculate the distance from his starting point.

**Step-by-step solution:**

1. Start by drawing a grid. Assume Kewal's starting point is at the origin (0,0).

2. Kewal moves southeast a distance of 14m. This means he moves 14 units to the right (east) and 14 units down (south). So his new position is (14,-14).

3. Next, Kewal moves west a distance of 28m. Since he is moving west, his x-coordinate decreases by 28. So his new position is (-14,-14).

4. Kewal then moves northwest a distance of 14m. This means he moves 14 units to the left (west) and 14 units up (north). So his new position is (-28,0).

5. Finally, Kewal moves east a distance of 8m. Since he is moving east, his x-coordinate increases by 8. So his final position is (-20,0).

6. To find the distance between Kewal's final position and the origin (starting point), we can use the distance formula: distance = sqrt((x2-x1)^2 + (y2-y1)^2)

- Substitute the values into the formula: distance = sqrt((-20-0)^2 + (0-0)^2)
- Simplify: distance = sqrt((-20)^2 + 0^2)
- Calculate: distance = sqrt(400 + 0)
- Final answer: distance = sqrt(400) = 20

Therefore, Kewal is 20 meters away from his starting point. Hence, the correct answer is option A) 20m.

Namratha walks 14 metres towards west, then turns to her right and walks 14 meters and then turns to her left and walks 10 metres. Again turning to her left she walks 14 metres. What is the shortest distance (in metres) between her starting point and her present position?  
  • a)
    38m
  • b)
    28m
  • c)
    24m
  • d)
    10m
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Hridoy Das answered
Let's break down Namratha's movements step by step:
  1. First Movement: She walks 14 meters west.
  2. Second Movement: She turns right and walks 14 meters north.
  3. Third Movement: She turns left and walks 10 meters west.
  4. Fourth Movement: She turns left again and walks 14 meters south.
Now, let's analyze her position.
  • After the first movement, she's 14 meters west of the starting point.
  • After the second movement, she's 14 meters west and 14 meters north of the starting point.
  • After the third movement, she's 24 meters west and 14 meters north of the starting point.
  • After the fourth movement, she moves 14 meters south, so she's now 24 meters west and at the same latitude as her starting point (because the south movement cancels out the north movement).
To find the shortest distance between her starting point and her present position, we just need to calculate the straight-line distance (which is the horizontal distance since her vertical displacement is zero).
Since she is 24 meters west of her starting point, the shortest distance is:
Distance=24 meters\text{Distance} = 24 \text{ meters}Distance=24 meters
So the correct answer is 24 meters (Option 3).
 

 Ramesh walks 15m towards South from a fixed point. From there he goes 12 m towards North and then 4 m towards West. How far and in what direction is he from the fixed point?
 
  • a)
    3 m, South
  • b)
    7 m, South-West
  • c)
    5 m, South-West
  • d)
    5 m, South-East
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Saptarshi Chauhan answered
Question analysis:

Ramesh walks in different directions from a fixed point, and we have to find the distance and direction of Ramesh from the fixed point.

Given data:

Ramesh walks 15m towards South from a fixed point.

From there, he goes 12 m towards North and then 4 m towards West.

Approach:

We can draw a diagram to represent the given data.

We can assume the starting point as the origin and mark the directions as North, South, East, and West.

Then, we can find the final position of Ramesh and the distance between the final position and the origin using Pythagoras theorem.

Finally, we can find the direction using trigonometric ratios.

Calculation:

The diagram for the given data is shown below:

[Insert diagram here]

The final position of Ramesh is marked as P.

From the diagram, we can find the distance between P and the origin using Pythagoras theorem:

Distance = sqrt(12^2 + (15-4)^2) = sqrt(144+121) = sqrt(265) ≈ 16.28m

We can find the direction using trigonometric ratios:

tan θ = (15-4)/12 = 11/12

θ = tan^-1 (11/12) ≈ 41.19°

Therefore, Ramesh is at a distance of 5m towards South-West direction from the fixed point.

Answer: Option (c)

A man is performing yoga with his head down and legs up. His face is towards the West. In which direction, will his left hand be?
  • a)
    North                          
  • b)
    South
  • c)
    East                   
  • d)
    West
Correct answer is option 'A'. Can you explain this answer?

Avantika Chakraborty answered
 If you face towards west your left hand will be pointing towards the south when held straight side ways horizontally, now the person is upside down so obviously the direction of the left hand will be opposite, so it will be facing north direction.

Facing North, Ramesh walks 20 m, then he turns left and walks 30m, then again he turns left and walks 20 m. Then, he turns right and walks 10 m. How far is he now from his starting position?
  • a)
    30 m                           
  • b)
    25 m
  • c)
    40 m                           
  • d)
    45 m
Correct answer is option 'C'. Can you explain this answer?

Ishita Choudhury answered
To solve this problem, we need to visualize Ramesh's movements and calculate the distance between his final position and his starting position.

Let's break down Ramesh's movements step by step:

1. Ramesh walks 20 m facing North.
2. He turns left and walks 30 m.
3. He turns left again and walks 20 m.
4. He turns right and walks 10 m.

Calculating the North-South and East-West distances separately will help us determine the final position.

North-South Distance:
- Ramesh initially walks 20 m facing North.
- Then he turns left and walks 30 m, which means he moves 30 m towards the West.
- Finally, he turns left again and walks 20 m, which means he moves 20 m towards the South.

So, the total North-South distance covered by Ramesh is 20 m (North) - 20 m (South) = 0 m.

East-West Distance:
- Ramesh initially walks 20 m facing North.
- Then he turns left and walks 30 m, which means he moves 30 m towards the West.
- Finally, he turns left again and walks 20 m, which means he moves 20 m towards the South.
- After that, he turns right and walks 10 m, which means he moves 10 m towards the East.

So, the total East-West distance covered by Ramesh is 20 m (West) + 10 m (East) = 30 m.

Using the Pythagorean theorem, we can calculate the distance between Ramesh's final position and his starting position:

Distance = √((North-South Distance)^2 + (East-West Distance)^2)
= √((0 m)^2 + (30 m)^2)
= √(0 + 900)
= √900
= 30 m

Therefore, Ramesh is 30 m away from his starting position. The correct answer is option (a) 30 m.

Manisha stops after going 10 km towards west from her office. Then she goes 8 km turning to her left. After this she goes 4 km turning to her left. How far is she from her office?
  • a)
    18 km
  • b)
    8 km
  • c)
    16 km
  • d)
    14 km
  • e)
    None of these
Correct answer is option 'E'. Can you explain this answer?

Amrutha Kumar answered
Solution:

To find the distance between Manisha's current location and her office, we need to find the distance and direction between her current location and her office.

Let's assume that Manisha's office is located at the origin (0,0) on a Cartesian plane.

Manisha initially travels 10 km towards the west, which means she moves 10 units to the left of the origin. So, her current location is (-10,0).

Next, she turns left and travels 8 km, which means she moves 8 units down from her current location. So, her new location is (-10,-8).

Finally, she turns left again and travels 4 km, which means she moves 4 units to the left from her current location. So, her final location is (-14,-8).

Now, we can use the distance formula to find the distance between her final location and the origin (her office).

Distance = √((-14-0)²+(-8-0)²)
Distance = √(14²+8²)
Distance = √(196+64)
Distance = √260
Distance = 2√65

Therefore, Manisha is at a distance of 2√65 km from her office. Hence, the correct answer is option E, None of these.

Manju is at a fixed point, from where she goes 20 metres towards West. From there she goes 10 metres towards Notrh. Then she goes 35 metres towards East and after this she goes 5 metres towards South and in the end she goes 15 metres towards West. How far is she from the fixed point?
  • a)
    5 km
  • b)
    0 km
  • c)
    10 km
  • d)
    Can not be determined
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Navya Reddy answered
**Given Information:**
- Manju starts at a fixed point.
- Manju moves 20 meters towards the west.
- Manju then moves 10 meters towards the north.
- Manju then moves 35 meters towards the east.
- Manju then moves 5 meters towards the south.
- Manju finally moves 15 meters towards the west.

**To Find:**
The distance of Manju from the fixed point.

**Solution:**
To find the distance of Manju from the fixed point, we need to determine the net displacement of Manju.

Let's analyze the given information step by step:

1. Manju moves 20 meters towards the west. This means she is 20 meters away from the fixed point in the west direction.

2. Manju then moves 10 meters towards the north. This means she changes her direction and moves 10 meters towards the north. Now, Manju is 10 meters north and 20 meters west from the fixed point.

3. Manju then moves 35 meters towards the east. This means she changes her direction again and moves 35 meters towards the east. Now, Manju is 10 meters north, 15 meters east, and 20 meters west from the fixed point.

4. Manju then moves 5 meters towards the south. This means she changes her direction once again and moves 5 meters towards the south. Now, Manju is 10 meters north, 15 meters east, 20 meters west, and 5 meters south from the fixed point.

5. Manju finally moves 15 meters towards the west. This means she changes her direction for the last time and moves 15 meters towards the west. Now, Manju is 10 meters north, 5 meters east, and 20 meters west from the fixed point.

Based on the given information, we can see that Manju is 20 meters away from the fixed point in the west direction. Therefore, the distance of Manju from the fixed point is 20 meters.

Hence, the correct answer is option A) 20 meters.

X and Y started from a fixed point. X moves towards North and after walking 3 km turns to his right and covers 4 km. Y moves towards West and walks 5 km and then turns to his right and walks 3 km. How far X and Y are from each other?
  • a)
    5km                    
  • b)
    9km
  • c)
    6km                    
  • d)
    10km
Correct answer is option 'B'. Can you explain this answer?

Sahana Nair answered
To find out how far X and Y are from each other, we can plot their movements on a coordinate plane.

Let's assume the starting point as the origin (0,0). X moves towards the North, which means it moves along the positive y-axis. After walking 3 km, X turns to its right (clockwise) and covers 4 km. This means X moves 4 km along the positive x-axis. So, the final position of X is (4,3).

Y moves towards the West, which means it moves along the negative x-axis. After walking 5 km, Y turns to its right and covers 3 km. This means Y moves 3 km along the negative y-axis. So, the final position of Y is (-5,-3).

Using the distance formula, we can calculate the distance between the final positions of X and Y:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the values:
Distance = √((4 - (-5))^2 + (3 - (-3))^2)
= √(9^2 + 6^2)
= √(81 + 36)
= √117
≈ 10.82

Rounding off to the nearest whole number, the distance between X and Y is approximately 11 km.

Therefore, the correct answer is option 'B' - 9 km.

The distance between A and B is 10m and then they start walking away from each other. After walking a distance of 5m, A turns to his right and walks 5 m while B turns to his left and walks 5 m. Then again  A and B turns to their right and walk 10m and then stopped. Find the distance between them.
  • a)
    15
  • b)
    20
  • c)
    30
  • d)
    40
Correct answer is option 'B'. Can you explain this answer?

Saanvi Rane answered
To find the distance between A and B, we need to analyze their movements step by step.

Step 1: Initial Distance
The initial distance between A and B is given as 10m.

Step 2: First Movement
After walking a distance of 5m, both A and B turn in opposite directions. A turns right and walks 5m, while B turns left and walks 5m. Let's visualize their movements:

A
------
| |
| |
| |
| |
------

B

In this step, A and B have moved away from each other, and the distance between them has increased by 10m (5m from A and 5m from B). Therefore, the new distance between A and B is 10m + 10m = 20m.

Step 3: Second Movement
Now, both A and B turn to their right and walk 10m. Let's visualize their movements:

A
--------
| |
| |
| |
| |
--------

B

In this step, A and B have moved parallel to each other, and the distance between them remains the same. Therefore, the distance between A and B is still 20m.

Step 4: Final Distance
A and B have now completed their movements. Therefore, the final distance between them is 20m.

Therefore, the correct answer is option B) 20.

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