ReasoningAbility.com

Distance Logic - Expert Level: directional distances EXPERT

Comprehensive self assessment worksheet covering 20 expert-level distance logic problems. Worksheet 28 of 30 emphasizes directional distances. Master path length, position finding, coordinate geometry through detailed explanations. Difficulty: challenging problems and time-bound practice. Tailored for expert-level preparation.

📝 Worksheet 28 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Expert level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 28 of 30 (93% complete)

Question 1

Two persons A and B start from the same point. A walks 6 m South, then 12 m East, then 18 m East. B walks 9 m South, then 12 m West. What is the distance between them?
Step-by-step:
1. A's final position: (30, -6)
2. B's final position: (-12, -9)
3. Distance = √[(30--12)² + (-6--9)²] = √[42² + 3²] = 42 m
two-persons, relative, distance

Question 2

A person walks 12 m East, then 21 m North, then 15 m West. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 21 m North
- East-West: -3 m West
2. Displacement = √(-3² + 21²) = √450 = 21 m
3. Total distance walked = 48 m
multi-stage, displacement, complex

Question 3

A person walks 17 m South, then 20 m South, then 10 m West. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: -37 m South
- East-West: -10 m West
2. Displacement = √(-10² + -37²) = √1469 = 38 m
3. Total distance walked = 47 m
multi-stage, displacement, complex

Question 4

A train 210 m long is running at 87 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 87 km/h = 24.2 m/s
2. Time = Length / Speed = 210 / 24.2 = 8.7 seconds
train, platform, pole, ssc

Question 5

Two persons A and B start from the same point. A walks 6 m North, then 13 m East. B walks 6 m South, then 6 m North. What is the distance between them?
Step-by-step:
1. A's final position: (13, 6)
2. B's final position: (0, 0)
3. Distance = √[(13-0)² + (6-0)²] = √[13² + 6²] = 14 m
two-persons, relative, distance

Question 6

A train 391 m long is running at 70 km/h. How long will it take to cross a 226 m long platform?
Step-by-step:
1. Speed = 70 km/h = 19.4 m/s
2. Total distance = Train length + Platform length = 391 + 226 = 617 m
3. Time = Distance / Speed = 617 / 19.4 = 31.7 seconds
train, platform, pole, ssc

Question 7

A train 299 m long is running at 59 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 59 km/h = 16.4 m/s
2. Time = Length / Speed = 299 / 16.4 = 18.2 seconds
train, platform, pole, ssc

Question 8

A runner runs at 7 m/s on a circular track of length 697 m for 137 seconds. How many laps does he complete?
Step-by-step:
1. Distance covered in 137 seconds = 7 × 137 = 959 m
2. Number of laps = Distance / Track length = 959 / 697 = 1.4 laps
circular, track, meeting, laps

Question 9

A train 318 m long is running at 74 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 74 km/h = 20.6 m/s
2. Time = Length / Speed = 318 / 20.6 = 15.5 seconds
train, platform, pole, ssc

Question 10

From point P, a person walks 8 m West, then 6 m South. 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 11

A boat travels 52 km downstream in 1.6 hours and upstream in 3.1 hours. The stream speed is 8 km/h. Find the boat's speed in still water.
Step-by-step:
1. Let boat speed = x km/h, stream speed = 8 km/h
2. Downstream: 52/(x + 8) = 1.6
3. Upstream: 52/(x - 8) = 3.1
4. Solving gives x = 25 km/h
boat, stream, upstream, downstream

Question 12

Two persons A and B start from the same point. A walks 14 m South, then 13 m West, then 11 m North. B walks 15 m East, then 8 m North, then 14 m West. What is the distance between them?
Step-by-step:
1. A's final position: (-13, -3)
2. B's final position: (1, 8)
3. Distance = √[(-13-1)² + (-3-8)²] = √[-14² + -11²] = 18 m
two-persons, relative, distance

Question 13

A person starts from point O and walks 11m West, then 10m West. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 11m West, then 10m West
2. Net position: (-21, 0)
3. Distance = √(-21² + 0²) = √441 = 21 m
basic, movement, straight-line

Question 14

Train A at 49 km/h and Train B at 77 km/h start from stations 524 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 = 49 + 77 = 126 km/h
2. Time = Distance / Relative Speed = 524 / 126 = 4.2 hours
relative, meeting, catch-up

Question 15

A boat travels 71 km downstream in 3.4 hours and upstream in 4.7 hours. The stream speed is 3 km/h. Find the boat's speed in still water.
Step-by-step:
1. Let boat speed = x km/h, stream speed = 3 km/h
2. Downstream: 71/(x + 3) = 3.4
3. Upstream: 71/(x - 3) = 4.7
4. Solving gives x = 18 km/h
boat, stream, upstream, downstream

Question 16

From point P, a person walks 7 m South, then 24 m West. What is the shortest distance from point P?
Step-by-step:
1. These movements form a right angle
2. Shortest distance = √(7² + 24²)
3. = √(49 + 576) = √625 = 25 m
pythagoras, right-angle, shortest-distance

Question 17

Two persons A and B start from the same point. A walks 11 m South, then 8 m East, then 12 m East. B walks 8 m South, then 12 m East. What is the distance between them?
Step-by-step:
1. A's final position: (20, -11)
2. B's final position: (12, -8)
3. Distance = √[(20-12)² + (-11--8)²] = √[8² + -3²] = 9 m
two-persons, relative, distance

Question 18

A person walks 21 m West, then 19 m West, then 24 m North. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 24 m North
- East-West: -40 m West
2. Displacement = √(-40² + 24²) = √2176 = 47 m
3. Total distance walked = 64 m
multi-stage, displacement, complex

Question 19

Two persons A and B start from the same point. A walks 15 m East, then 5 m East, then 16 m North. B walks 17 m North, then 18 m East, then 16 m East. What is the distance between them?
Step-by-step:
1. A's final position: (20, 16)
2. B's final position: (34, 17)
3. Distance = √[(20-34)² + (16-17)²] = √[-14² + -1²] = 14 m
two-persons, relative, distance

Question 20

A person travels at 35 km/h for 2 hours and then at 80 km/h for 2 hours. What is the average speed?
Step-by-step:
1. For equal time intervals, Average Speed = (v1 + v2) / 2
2. = (35 + 80) / 2 = 57.5 km/h
average, speed, distance
Previous Worksheet Next Worksheet