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Distance Logic - Intermediate Level: angular distances INTERMEDIATE

Boost your speed and accuracy with this adaptive style 📈 worksheet. Worksheet 15 of 30 presents 20 intermediate-level distance logic problems. Focus on angular distances while practicing distance calculation, shortest path, displacement problems. Difficulty: moderate complexity with mixed patterns. Perfect for mid-level test takers.

📝 Worksheet 15 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 15 of 30 (50% complete)

Question 1

Two persons A and B start from the same point. A walks 18 m North, then 19 m North, then 11 m North. B walks 8 m South, then 10 m North, then 8 m North. What is the distance between them?
Step-by-step:
1. A's final position: (0, 48)
2. B's final position: (0, 10)
3. Distance = √[(0-0)² + (48-10)²] = √[0² + 38²] = 38 m
two-persons, relative, distance

Question 2

Train A at 62 km/h and Train B at 66 km/h start from stations 345 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 = 62 + 66 = 128 km/h
2. Time = Distance / Relative Speed = 345 / 128 = 2.7 hours
relative, meeting, catch-up

Question 3

A person starts from point O and walks 21m East, then 9m East. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 21m East, then 9m East
2. Net position: (30, 0)
3. Distance = √(30² + 0²) = √900 = 30 m
basic, movement, straight-line

Question 4

Two persons A and B start from the same point. A walks 16 m South, then 7 m North. B walks 7 m East, then 10 m East, then 7 m East. What is the distance between them?
Step-by-step:
1. A's final position: (0, -9)
2. B's final position: (24, 0)
3. Distance = √[(0-24)² + (-9-0)²] = √[-24² + -9²] = 26 m
two-persons, relative, distance

Question 5

A person starts from point O and walks 15m North, then 12m North. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 15m North, then 12m North
2. Net position: (0, 27)
3. Distance = √(0² + 27²) = √729 = 27 m
basic, movement, straight-line

Question 6

A train 183 m long is running at 69 km/h. How long will it take to cross a 192 m long platform?
Step-by-step:
1. Speed = 69 km/h = 19.2 m/s
2. Total distance = Train length + Platform length = 183 + 192 = 375 m
3. Time = Distance / Speed = 375 / 19.2 = 19.6 seconds
train, platform, pole, ssc

Question 7

From point X, a person goes 15 m East, then 20 m North. What is the shortest distance from point X?
Step-by-step:
1. The path forms a right triangle
2. Shortest distance = √(15² + 20²) = √625 = 25 m
shortest-path, pythagoras

Question 8

A train 358 m long is running at 67 km/h. How long will it take to cross a 248 m long platform?
Step-by-step:
1. Speed = 67 km/h = 18.6 m/s
2. Total distance = Train length + Platform length = 358 + 248 = 606 m
3. Time = Distance / Speed = 606 / 18.6 = 32.6 seconds
train, platform, pole, ssc

Question 9

Two persons A and B start from the same point. A walks 16 m West, then 18 m West, then 16 m North. B walks 20 m North, then 18 m North, then 18 m North. What is the distance between them?
Step-by-step:
1. A's final position: (-34, 16)
2. B's final position: (0, 56)
3. Distance = √[(-34-0)² + (16-56)²] = √[-34² + -40²] = 52 m
two-persons, relative, distance

Question 10

Train A at 59 km/h and Train B at 57 km/h start from stations 395 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 = 59 + 57 = 116 km/h
2. Time = Distance / Relative Speed = 395 / 116 = 3.4 hours
relative, meeting, catch-up

Question 11

Two runners start from the same point on a circular track of length 680 m. Their speeds are 12 m/s and 15 m/s. If they run in the same direction, when will they meet again?
Step-by-step:
1. Relative speed (same direction) = |15 - 12| = 3 m/s
2. Time to meet = Track length / Relative speed = 680 / 3 = 226.7 seconds
circular, track, meeting, laps

Question 12

A person travels 9 m West, then 12 m South. Find the shortest distance from the starting point.
Step-by-step:
1. West and South are perpendicular directions
2. Shortest distance = √(9² + 12²) = √225 = 15 m
shortest-path, pythagoras

Question 13

Two persons A and B start from the same point. A walks 19 m South, then 17 m West, then 5 m East. B walks 15 m North, then 13 m North, then 13 m South. What is the distance between them?
Step-by-step:
1. A's final position: (-12, -19)
2. B's final position: (0, 15)
3. Distance = √[(-12-0)² + (-19-15)²] = √[-12² + -34²] = 36 m
two-persons, relative, distance

Question 14

Car A at 56 km/h and Car B at 79 km/h start from the same point in the same direction. How long will it take for them to be 386 km apart?
Step-by-step:
1. Relative speed when moving in same direction = |79 - 56| = 23 km/h
2. Time = Distance / Relative Speed = 386 / 23 = 16.8 hours
3. The second car will be 386 km ahead after 16.8 hours
relative, meeting, catch-up

Question 15

A boat travels at 24 km/h in still water. Stream speed is 8 km/h. What is the difference between upstream and downstream time for 39 km?
Step-by-step:
1. Downstream speed = 32 km/h, Time = 1.2 hours
2. Upstream speed = 16 km/h, Time = 2.4 hours
3. Difference = 2.4 - 1.2 = 1.2 hours
boat, stream, upstream, downstream

Question 16

From point P, a person walks 5 m South, then 12 m West. 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 17

A person starts from point O and walks 19m North, then 24m North. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 19m North, then 24m North
2. Net position: (0, 43)
3. Distance = √(0² + 43²) = √1849 = 43 m
basic, movement, straight-line

Question 18

A runner runs at 8 m/s on a circular track of length 409 m for 129 seconds. How many laps does he complete?
Step-by-step:
1. Distance covered in 129 seconds = 8 × 129 = 1032 m
2. Number of laps = Distance / Track length = 1032 / 409 = 2.5 laps
circular, track, meeting, laps

Question 19

A person walks 19 m West, then 23 m South, then 10 m South. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: -33 m South
- East-West: -19 m West
2. Displacement = √(-19² + -33²) = √1450 = 38 m
3. Total distance walked = 52 m
multi-stage, displacement, complex

Question 20

A boat travels 78 km downstream in 3.7 hours and upstream in 15.6 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: 78/(x + 8) = 3.7
3. Upstream: 78/(x - 8) = 15.6
4. Solving gives x = 13 km/h
boat, stream, upstream, downstream
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