Direction and distance
- Q is 12 m east of P. R is 16 m north of Q. How far is P from R, and in which direction is P with respect to R?(Use the eight main directions: a place that is both north and east of another is taken to be north-east of it, and so on.) Answer: D. 20 m, south-west Answer: (D) 20 m, south-west P = (0, 0), Q = (12, 0), R = (12, 16). PR = √(12² + 16²) = 20 m. From R, P is to th... 1
- Anil walks 5 km towards the north, then turns right and walks 3 km. In which direction is he facing now? Answer: C. East Answer: (C) East When you face north, your right hand points east. After turning right he walks, and keeps facing, east. 1
- Priya walks 6 km east and then turns left and walks 8 km. How far is she from her starting point? Answer: B. 10 km Answer: (B) 10 km Facing east, a left turn means north. So she is 6 km east and 8 km north of the start. Distance = √(6² +... 1
- A boy is facing north. He turns right, and then turns right again. In which direction is he facing now? Answer: A. South Answer: (A) South North → right → East → right → South. Two right turns make a 180° turn. 1
- Ravi walks 4 km towards the south, then turns to his left and walks 3 km. In which direction is he facing now? Answer: A. East Answer: (A) East When you face south, your left hand points east. So after the left turn he faces east. 1
- A is 5 m to the north of B. C is 5 m to the east of B. In which direction is C with respect to A? Answer: D. South-east Answer: (D) South-east Put B at the origin. A is at (0, 5) and C is at (5, 0). From A, C is 5 m east and 5 m south, so... 1
- Early one morning, Rohan stood facing the rising sun. In which direction did his shadow fall? Answer: B. Behind him, towards the west Answer: (B) Behind him, towards the west The sun rises in the east, so Rohan faces east. A shadow fa... 1
- Sunita walks 20 m towards the north, turns right and walks 10 m, then turns right again and walks 20 m. Where is she now with respect to her starting point? Answer: C. 10 m east Answer: (C) 10 m east North 20 m, right (east) 10 m, right (south) 20 m. The 20 m north and 20 m south cancel out. She... 1
- A man walks 3 km east, then turns left and walks 4 km, then turns left again and walks 3 km. Where is he now with respect to his starting point? Answer: C. 4 km north Answer: (C) 4 km north East 3 km, left (north) 4 km, left (west) 3 km. The 3 km east and 3 km west cancel out, so he i... 1
- A girl is facing west. She turns 135° in the anticlockwise direction. In which direction is she facing now? Answer: B. South-east Answer: (B) South-east Anticlockwise from west: 45° → south-west, 90° → south, 135° → south-east. 1
- Sita walks 12 m south, then turns left and walks 5 m. What is the shortest distance between her and her starting point? Answer: A. 13 m Answer: (A) 13 m Facing south, a left turn is east. She is 12 m south and 5 m east of the start. Distance = √(12² + 5²) = √(... 1
- Starting from a point, Vikram walks 15 m north, turns right and walks 10 m, turns right and walks 7 m, then turns left and walks 5 m. How far is he from the starting point? Answer: A. 17 m Answer: (A) 17 m North 15 m → (0, 15). Right = east 10 m → (10, 15). Right = south 7 m → (10, 8). Left = east 5 m → (15, 8).... 1
- P is 6 m to the west of Q. R is 8 m to the south of Q. What is the distance between P and R? Answer: B. 10 m Answer: (B) 10 m Put Q at the origin: P = (−6, 0), R = (0, −8). PR = √(6² + 8²) = 10 m. 1
- One evening, Ajay and Vijay were talking, facing each other. Ajay’s shadow fell exactly to his right. Which direction was Ajay facing? Answer: C. North Answer: (C) North In the evening the sun is in the west, so shadows fall towards the east. Ajay’s right is east. A person w... 1
- A man is facing south. He turns 45° clockwise and then 180° anticlockwise. Which direction is he facing now? Answer: C. North-east Answer: (C) North-east Clockwise from south: 45° → south-west. A 180° turn (either way) faces the opposite direction:... 1
- Kunal walks 30 m north, turns left and walks 40 m, then turns left again and walks 30 m. Where is he with respect to his starting point? Answer: D. 40 m west Answer: (D) 40 m west North 30 m, left (west) 40 m, left (south) 30 m. North and south cancel out, so he is 40 m west o... 1
- Town B is 9 km east of town A. Town C is 7 km north of B, and town D is 5 km north of C. What is the straight-line distance between A and D? Answer: A. 15 km Answer: (A) 15 km D is 7 + 5 = 12 km north of B, and B is 9 km east of A. AD = √(9² + 12²) = √(225) = 15 km. 1
- X is to the south of Y, and Z is to the east of Y. In which direction is X with respect to Z?(Use the eight main directions: a place that is both north and east of another is taken to be north-east of it, and so on.) Answer: A. South-west Answer: (A) South-west Put Y at the origin. X is somewhere below it and Z somewhere to its right. From Z, X is to the... 1
- If north-east is called west, west is called south-east and so on (all directions turned the same way), what will south be called? Answer: A. North-east Answer: (A) North-east North-east → west is a turn of 225° clockwise (or 135° anticlockwise). Check: west → south-east... 1
- Meena walks 5 km south, turns right and walks 3 km, then turns left and walks 5 km. Where is she with respect to the starting point? Answer: C. 10 km south and 3 km west Answer: (C) 10 km south and 3 km west Facing south, right is west: she walks 3 km west. Then left turns... 1
- A and B start from the same point. A walks 12 km west, then turns left and walks 5 km. B walks 3 km east, then turns left and walks 3 km. What is the distance between A and B now? Answer: D. 17 km Answer: (D) 17 km A: west 12, then left (south) 5 → (−12, −5). B: east 3, then left (north) 3 → (3, 3). Gap: 15 km east–wes... 1
- Starting from point P, Nitin walks 20 m north, turns right and walks 30 m, turns right and walks 35 m, turns left and walks 15 m, and then turns left and walks 15 m. How far and in which direction is he from P? Answer: B. 45 m east Answer: (B) 45 m east N 20 → (0, 20). Right = E 30 → (30, 20). Right = S 35 → (30, −15). Left = E 15 → (45, −15). Left... 1
- At 7 a.m., Mohan was walking towards his own shadow. He then turned left and walked a little, and then turned left again. Which direction is he facing now? Answer: B. East Answer: (B) East At 7 a.m. the sun is in the east, so shadows fall to the west. Walking towards his shadow, he faces west. W... 1
- ‘P % Q’ means P is 4 m to the north of Q, and ‘P & Q’ means P is 3 m to the east of Q. If A % B & C, what is the position of A with respect to C?(Use the eight main directions: a place that is both north and east of another is taken to be north-east… Answer: D. 5 m to the north-east Answer: (D) 5 m to the north-east B & C: B is 3 m east of C. A % B: A is 4 m north of B. So A is 3 m east a... 1