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Distance Logic - Expert Level: angular distances EXPERT

Intensive progress check 🎯 drill: 20 expert-level distance logic questions. Worksheet 30 of 30 hones your angular distances abilities. Practice shortest path, displacement problems, route mapping under timed conditions. Best for expert-level students seeking challenging problems and time-bound practice.

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

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 30 of 30 (100% complete)

Question 1

Two runners start from the same point on a circular track of length 735 m. Their speeds are 10 m/s and 14 m/s. If they run in opposite directions, when will they meet?
Step-by-step:
1. Relative speed (opposite direction) = 10 + 14 = 24 m/s
2. Time to meet = Track length / Relative speed = 735 / 24 = 30.6 seconds
circular, track, meeting, laps

Question 2

A boat travels at 12 km/h in still water. Stream speed is 4 km/h. What is the difference between upstream and downstream time for 50 km?
Step-by-step:
1. Downstream speed = 16 km/h, Time = 3.1 hours
2. Upstream speed = 8 km/h, Time = 6.2 hours
3. Difference = 6.2 - 3.1 = 3.1 hours
boat, stream, upstream, downstream

Question 3

A person walks 9 m South, then 18 m South, then 12 m East, then 21 m West. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: -27 m South
- East-West: -9 m West
2. Displacement = √(-9² + -27²) = √810 = 28 m
3. Total distance walked = 60 m
multi-stage, displacement, complex

Question 4

Two persons A and B start from the same point. A walks 5 m West, then 15 m South. B walks 17 m North, then 9 m East. What is the distance between them?
Step-by-step:
1. A's final position: (-5, -15)
2. B's final position: (9, 17)
3. Distance = √[(-5-9)² + (-15-17)²] = √[-14² + -32²] = 35 m
two-persons, relative, distance

Question 5

A boat travels at 16 km/h in still water. The stream flows at 5 km/h. How long will it take to go 79 km downstream?
Step-by-step:
1. Downstream speed = Boat speed + Stream speed = 16 + 5 = 21 km/h
2. Time = Distance / Speed = 79 / 21 = 3.8 hours
boat, stream, upstream, downstream

Question 6

Car A at 47 km/h and Car B at 70 km/h start from the same point in the same direction. How long will it take for them to be 390 km apart?
Step-by-step:
1. Relative speed when moving in same direction = |70 - 47| = 23 km/h
2. Time = Distance / Relative Speed = 390 / 23 = 17.0 hours
3. The second car will be 390 km ahead after 17.0 hours
relative, meeting, catch-up

Question 7

A person walks from a point where his shadow length is measured to another point. The distances from a lamp post are 48 m and 84 m respectively. How far did he walk?
Step-by-step:
1. First position: distance from pole = 48 m
2. Second position: distance from pole = 84 m
3. Distance between positions = 84 - 48 = 36 m
shadow, similar-triangles, ssc

Question 8

A car travels at 57 km/h for 6 hours. What distance does it cover?
Distance = Speed × Time = 57 × 6 = 342 km
speed, time, basic

Question 9

A person starts from point O and walks 13m East, then 22m East, then 23m West. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 13m East, then 22m East, then 23m West
2. Net position: (12, 0)
3. Distance = √(12² + 0²) = √144 = 12 m
basic, movement, straight-line

Question 10

A person walks 7 m North, then 24 m East. What is the straight-line distance from the starting point?
Step-by-step:
1. These are perpendicular movements
2. Straight-line distance = √(7² + 24²) = √625 = 25 m
shortest-path, pythagoras

Question 11

A boat travels at 18 km/h in still water. Stream speed is 8 km/h. What is the difference between upstream and downstream time for 60 km?
Step-by-step:
1. Downstream speed = 26 km/h, Time = 2.3 hours
2. Upstream speed = 10 km/h, Time = 6.0 hours
3. Difference = 6.0 - 2.3 = 3.7 hours
boat, stream, upstream, downstream

Question 12

A train 251 m long is running at 65 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 65 km/h = 18.1 m/s
2. Time = Length / Speed = 251 / 18.1 = 13.9 seconds
train, platform, pole, ssc

Question 13

A person walks 16 m West, then 20 m East, then 16 m East, then 11 m North. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 11 m North
- East-West: 20 m East
2. Displacement = √(20² + 11²) = √521 = 23 m
3. Total distance walked = 63 m
multi-stage, displacement, complex

Question 14

A person travels from A to B at 44 km/h and returns at 58 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 × 44 × 58) / (44 + 58)
3. = 5104 / 102 = 50.0 km/h
average, speed, distance

Question 15

A train 316 m long is running at 82 km/h. How long will it take to cross a 278 m long platform?
Step-by-step:
1. Speed = 82 km/h = 22.8 m/s
2. Total distance = Train length + Platform length = 316 + 278 = 594 m
3. Time = Distance / Speed = 594 / 22.8 = 26.1 seconds
train, platform, pole, ssc

Question 16

A boat travels at 21 km/h in still water. Stream speed is 3 km/h. What is the difference between upstream and downstream time for 75 km?
Step-by-step:
1. Downstream speed = 24 km/h, Time = 3.1 hours
2. Upstream speed = 18 km/h, Time = 4.2 hours
3. Difference = 4.2 - 3.1 = 1.1 hours
boat, stream, upstream, downstream

Question 17

A boat travels at 16 km/h in still water. Stream speed is 3 km/h. What is the difference between upstream and downstream time for 32 km?
Step-by-step:
1. Downstream speed = 19 km/h, Time = 1.7 hours
2. Upstream speed = 13 km/h, Time = 2.5 hours
3. Difference = 2.5 - 1.7 = 0.8 hours
boat, stream, upstream, downstream

Question 18

A train moves at 56 km/h for 15 minutes. What distance does it cover?
Time = 15 minutes = 0.25 hours
Distance = 56 × 0.25 = 14.0 km
speed, time, basic

Question 19

A 150 cm tall person casts a 193 cm shadow. A nearby building is 567 cm tall. How long will its shadow be?
Step-by-step:
1. Ratio of height to shadow length = 150/193 = 0.78
2. For object: Height / Shadow = 0.78
3. Shadow = Height / Ratio = 567 / 0.78 = 729.5 cm
shadow, similar-triangles, ssc

Question 20

From point P, a person walks 9 m East, then 12 m North. 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
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