# Worked Examples

Rohan walks 5 km towards north. Then he turns towards right and walks 3 km. Then he again turns to his right and moves 5 km. How far is he from the starting point?

- 10 km
- 13 km
- 15 km
- 8 km
- 3 km

The movements can be sketched in the form of an adjacent diagram.

Consider A as the starting point and B as the final point.

The shortest distance between A and B is 3 km.

**Answer:** (5)

Sanjay walks 7 km towards north and turns towards left and covers 3 km. Again he turns towards left and walks 11 km. How far is he from the starting point?

- 16 km
- 21 km
- 12 km
- 5 km
- 8 km

Sanjay started from A and walks 7 km north up to B, turns towards left (west) and goes 3 km to C and walks towards left (south) and walks 11 km and reaches point E.

Now DA = CB = 3 km

DC = AB = 7 km

DE = 11 â€“ DC = 4 km

DA = 3 km

DE = 4 km

EA =

**Answer:** (4)

Sushma walks 20 m towards north. Then she turns right and walks 30 m. Now, she turns right and walks 35 m. Now turning left, she walks 15 m. Again she turns left and moves 15 m. Finally, she turns left and walks 15 m. In which direction and how far is she from her original position?

- 15 m east
- 30 m east
- 15 m west
- 45 m west
- None of these

Sushma starts from A and after all the movements as per the directions given in the problem; she finally reaches the destination B. Now, she is at a distance of 30 m in the eastern direction from her starting point.

**Answer:** (2)

Akshatha walks 10 m facing the early morning Sun and goes 10 m to the right. She then walks 5, 15 and 15 m, each time turning to her left. How far is she now from her starting point?

- 10 m
- 15 m
- 20 m
- 5 m
- None of these

A is the starting point.

G is the final point.

DF = 15 m.

DE = CB = 10 m.

EF = DF â€“ DE = 15 â€“ 10 = 5 m.

AG = EF = 5 m.

**Answer:** (4)

In the adjacent figure, A, B, C and D are four persons stationed at the four corners of a square piece of plot. From the positions shown in the figure, C and A move diagonally to opposite corners and then walk one side each, clockwise direction and anticlockwise direction, respectively, along the sides. B and D move two sides each clockwise and anticlockwise, respectively.

What is the new position of A?

- Northern corner
- Western corner
- Southern corner
- Eastern corner
- Midway between original position of B and D

The movements of A and C and their final position are shown in diagram (i).

(i)

The movements of B and D and their final position are shown in diagram (ii).

(ii)

Now, the final positions of A, B, C and D are as shown in diagram (iii).

(iii)

Now, you can deduce that A is in the southern corner.

**Answer:** (3)

In the adjacent figure, A, B, C and D are four persons stationed at the four corners of a square field. From the positions given in the figure, A, B, C and D walk across the field, along the diagonals and reach the opposite corners. From these positions, A and D walk in the clockwise direction along the sides, whereas B and C walk in the anticlockwise direction along the sides. Each one covers half of a side.

Based on the above movements indicate which of the following statements is correct?

- D is to the north of B
- A is to the southwest of D
- A is to the northwest of B
- B is to the northeast of A
- C is to the northwest of B

The positions of A, B, C and D after the first part of their movements are as shown in the adjacent diagram (i).

(i)

The second part of their movements and their final positions are as shown in the diagrams (ii) and (iii), respectively.

(ii)

From diagram (iii), we observe that B is to the northeast of A.

(iii)

**Answer:** (4)

Four persons A, B, C and D are stationed at the four corners of a square piece of plot as shown in the diagram.

From the positions shown above, A starts crossing the field diagonally. After walking half of the distance, he/she turns right, walks some distance and turns left.

Which direction is A facing now?

- Northeast
- Northwest
- Southeast
- Southwest
- North

Movements of A is indicated in the diagram.

From the diagram, we can notice that A is facing northwest.

**Answer:** (2)

Four persons A, B, C and D are stationed at the four corners of a square piece of plot as shown in the diagram.

From the original position given in the diagram, A and B move one side length clockwise and then crossover to the corner diagonally opposite. C and D move one arm length anticlockwise and crossover to the corner diagonally opposite. The original configuration ADBC has now been changed to:

- CBDA
- BDAC
- DACB
- ACBD
- BCAD

The original and final positions of A, B, C and D are indicated in diagrams (i) and (ii), respectively.

(i) | (ii) |

The final positions of A, B, C and D are marked as A

^{*}B

^{*}C

^{*}D

^{*}. From diagram (ii), we observe that the original configuration ADBC has been changed to CBDA.

**Answer:**(1)

Four persons A, B, C and D are stationed at the four corners of a square piece of plot as shown in the diagram.

From the original position given in the diagram, D and B move one and a half length of sides in the clockwise and anticlockwise directions, respectively. Which one of the following statements is correct?

- Both B and D are at the mid-point between A and C.
- D is at mid-point between A and C; and B at the corner originally occupied by C.
- B is at mid-point between A and C; and D at the corner originally occupied by A.
- Both B and D are at the mid point between A and the original position of D.
- B is at the mid-point between A and the original position of D; and D is at the mid-point between the original position of B and C.

(i) | (ii) |

After the movements, the final positions of A, B, C and D are as shown in diagram (ii). We observe that B is at the mid-point between A and the original position of D and D is at the mid-point between the original position of B and C.

**Answer:** (5)

From the positions in the original figure, A and C move diagonally to opposite corners and then move one side each clockwise and anticlockwise, respectively. D and B move two sides each clockwise and anticlockwise, respectively. Where is A now?

- At the northwest corner
- At the southeast corner
- At the northeast corner
- At the southwest corner
- Midway between original position of B and D

The original and final positions of A, B, C and D are shown in diagrams (i) and (ii), respectively. We can deduce that A is at the northeast corner.

(i)

(ii)

**Answer:** (3)

A, B, C, D, E, F and G are seven places on a map. The following places are connected by two-way roads: A and B; A and F; C and F; C and D; F and G; D and E; B and C and E and G. No other roads prevail.

- Which is the shortest route (route with least number of intermediate places) from A to G?
1. A â€“ C â€“ G 2. A â€“ E â€“ G 3. A â€“ F â€“ G 4. A â€“ B â€“ G - If F to G and D to C are the only one-way routes, then which of the following places loses contact with A?
1. G 2. E 3. D 4. No place loses contact with A - How many distinct routes exist from D to F (without touching any place more than once)?
1. 2 2. 4 3. 1 4. 3 - The route covering the maximum number of places and going from A to C does not pass through _________.
1. E 2. D 3. B 4. F - If the number of places to which a place is connected directly is considered as the measure of importance, then which of the following places is of the highest importance?
1. D 2. B 3. C 4. A

Solution

Based on the conditions given in the problem, the route map of the places is as follows:

- As we see A â€“ F â€“ G is the shortest way (with only one intermediate point) from A to G.
**Answer:**(3) - If F to G and D to C are the only one-way routes, from the above figure, we see that from all places one can still reach A. Hence, none of the places loses contact with A.
**Answer:**(4) - To travel from D to F the routes available are: D â€“ C â€“ F; D â€“ E â€“ G â€“ F and D â€“ C â€“ B â€“ A â€“ F. So, three routes exist.
**Answer:**(4) - First let us try to find out a route from A to C with the maximum number of intermediate points. By observation, we find that it is A â€“ F â€“ G â€“ E â€“ D â€“ C. It does not touch B.
**Answer:**(3) - For each of the places given in the alternatives, B, A, C and D, let us observe how many places are directly connected.
**Answer:**(3)

Rahul starts from his bank at 5:00 p.m. and collect sweets from a shop where he spends 5 min. Then he goes to his friendâ€™s house to drop him. He immediately goes to the railway station. Then he realizes that he had left the sweet box with his friend. He goes back to his friendâ€™s house and chat with his friendâ€™s sister for 10 min and then starts for home. Rahul goes everywhere on his Scooty at an average speed of 20 km/h. Route connecting different places is shown in the adjacent figure. Each line segment represented by is 1 km.

- What was the total distance covered by Rahul from his bank to his home?
- 12 km
- 11 km
- 15 km
- 16 km
- 9 km

- How many minutes did he take in reaching home after reaching railway station?
- 20 min
- 15 min
- 30 min
- 25 min
- 17 min

- How much time he would have taken, if he had come home directly from the bank without going anywhere?
- 15 min
- 10 min
- 20 min
- 16 min
- 12 min

- Bank to Sweet shop 2 km
**Answer:**(2) - He has covered a distance of 5 km from the railway station to his house.
**Answer:**(4) - The direct distance from the bank to his house is 5 km.
**Answer****:**(1)