ReasoningAbility.com

Distance Logic - Advanced Level: coordinate geometry ADVANCED

Level up your distance logic skills with this challenging mix. 20 advanced-level problems await in Worksheet 24 of 30. Focus area: coordinate geometry. Learn displacement problems, route mapping, distance measurement through systematic practice. Designed for advanced learners seeking complex scenarios and multi-step problems.

📝 Worksheet 24 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 24 of 30 (80% complete)

Question 1

From point P, a person walks 5 m West, then 12 m South. What is the shortest distance from point P?
Step-by-step:
1. These movements form a right angle
2. Shortest distance = √(5² + 12²)
3. = √(25 + 144) = √169 = 13 m
pythagoras, right-angle, shortest-distance

Question 2

A person travels from A to B at 32 km/h and returns at 65 km/h. What is the average speed for the entire journey?
Step-by-step:
1. For equal distances, Average Speed = (2 × v1 × v2) / (v1 + v2)
2. = (2 × 32 × 65) / (32 + 65)
3. = 4160 / 97 = 42.9 km/h
average, speed, distance

Question 3

A 178 cm tall person casts a 273 cm shadow. A building casts a 561 cm shadow at the same time. How tall is the building?
Step-by-step:
1. Ratio of shadow to height = 273/178 = 1.53
2. For object: Shadow / Height = 1.53
3. Height = Shadow / Ratio = 561 / 1.53 = 365.8 cm
shadow, similar-triangles, ssc

Question 4

Two persons A and B start from the same point. A walks 17 m West, then 18 m North, then 15 m West. B walks 6 m East, then 14 m North, then 11 m East. What is the distance between them?
Step-by-step:
1. A's final position: (-32, 18)
2. B's final position: (17, 14)
3. Distance = √[(-32-17)² + (18-14)²] = √[-49² + 4²] = 49 m
two-persons, relative, distance

Question 5

Two persons A and B start from the same point. A walks 15 m South, then 13 m North. B walks 8 m West, then 15 m West. What is the distance between them?
Step-by-step:
1. A's final position: (0, -2)
2. B's final position: (-23, 0)
3. Distance = √[(0--23)² + (-2-0)²] = √[23² + -2²] = 23 m
two-persons, relative, distance

Question 6

Two persons A and B start from the same point. A walks 7 m South, then 17 m North. B walks 18 m South, then 9 m North. What is the distance between them?
Step-by-step:
1. A's final position: (0, 10)
2. B's final position: (0, -9)
3. Distance = √[(0-0)² + (10--9)²] = √[0² + 19²] = 19 m
two-persons, relative, distance

Question 7

A person walks 15 m North, then 20 m East. What is the straight-line distance from the starting point?
Step-by-step:
1. These are perpendicular movements
2. Straight-line distance = √(15² + 20²) = √625 = 25 m
shortest-path, pythagoras

Question 8

From point P, a person walks 8 m East, then 6 m North. What is the shortest distance from point P?
Step-by-step:
1. These movements form a right angle
2. Shortest distance = √(8² + 6²)
3. = √(64 + 36) = √100 = 10 m
pythagoras, right-angle, shortest-distance

Question 9

Train A at 41 km/h and Train B at 53 km/h start from stations 400 km apart and move towards each other. How long will they take to meet?
Step-by-step:
1. Relative speed when moving towards each other = 41 + 53 = 94 km/h
2. Time = Distance / Relative Speed = 400 / 94 = 4.3 hours
relative, meeting, catch-up

Question 10

From point P, a person walks 9 m North, then 12 m East. What is the shortest distance from point P?
Step-by-step:
1. These movements form a right angle
2. Shortest distance = √(9² + 12²)
3. = √(81 + 144) = √225 = 15 m
pythagoras, right-angle, shortest-distance

Question 11

A person walks 21 m North, then 23 m South, then 19 m East, then 8 m North. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 6 m North
- East-West: 19 m East
2. Displacement = √(19² + 6²) = √397 = 20 m
3. Total distance walked = 71 m
multi-stage, displacement, complex

Question 12

A train moves at 41 km/h for 30 minutes. What distance does it cover?
Time = 30 minutes = 0.5 hours
Distance = 41 × 0.5 = 20.5 km
speed, time, basic

Question 13

Two runners start from the same point on a circular track of length 599 m. Their speeds are 5 m/s and 14 m/s. If they run in opposite directions, when will they meet?
Step-by-step:
1. Relative speed (opposite direction) = 5 + 14 = 19 m/s
2. Time to meet = Track length / Relative speed = 599 / 19 = 31.5 seconds
circular, track, meeting, laps

Question 14

A train 314 m long is running at 89 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 89 km/h = 24.7 m/s
2. Time = Length / Speed = 314 / 24.7 = 12.7 seconds
train, platform, pole, ssc

Question 15

From point P, a person walks 8 m East, then 6 m North. What is the shortest distance from point P?
Step-by-step:
1. These movements form a right angle
2. Shortest distance = √(8² + 6²)
3. = √(64 + 36) = √100 = 10 m
pythagoras, right-angle, shortest-distance

Question 16

A person travels 7 m West, then 24 m South. Find the shortest distance from the starting point.
Step-by-step:
1. West and South are perpendicular directions
2. Shortest distance = √(7² + 24²) = √625 = 25 m
shortest-path, pythagoras

Question 17

A person walks 16 m West, then 18 m South, then 8 m South. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: -26 m South
- East-West: -16 m West
2. Displacement = √(-16² + -26²) = √932 = 31 m
3. Total distance walked = 42 m
multi-stage, displacement, complex

Question 18

Two runners start from the same point on a circular track of length 500 m. Their speeds are 12 m/s and 8 m/s. If they run in the same direction, when will they meet again?
Step-by-step:
1. Relative speed (same direction) = |8 - 12| = 4 m/s
2. Time to meet = Track length / Relative speed = 500 / 4 = 125.0 seconds
circular, track, meeting, laps

Question 19

A boat travels at 23 km/h in still water. The stream flows at 6 km/h. How long will it take to go 76 km downstream?
Step-by-step:
1. Downstream speed = Boat speed + Stream speed = 23 + 6 = 29 km/h
2. Time = Distance / Speed = 76 / 29 = 2.6 hours
boat, stream, upstream, downstream

Question 20

A car travels at 45 km/h for 4 hours. What distance does it cover?
Distance = Speed × Time = 45 × 4 = 180 km
speed, time, basic
Previous Worksheet Next Worksheet