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Distance Logic - Intermediate Level: directional distances INTERMEDIATE

Exam-focused quick response training ★ worksheet: 20 intermediate-level distance logic questions. Worksheet 13 of 30 targets directional distances. Build proficiency in relative distances, path length, position finding with detailed solutions. Ideal for mid-level competitive exam preparation.

📝 Worksheet 13 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 13 of 30 (43% complete)

Question 1

A person travels at 34 km/h for 2 hours and then at 70 km/h for 2 hours. What is the average speed?
Step-by-step:
1. For equal time intervals, Average Speed = (v1 + v2) / 2
2. = (34 + 70) / 2 = 52.0 km/h
average, speed, distance

Question 2

Two runners start from the same point on a circular track of length 696 m. Their speeds are 10 m/s and 9 m/s. If they run in opposite directions, when will they meet?
Step-by-step:
1. Relative speed (opposite direction) = 10 + 9 = 19 m/s
2. Time to meet = Track length / Relative speed = 696 / 19 = 36.6 seconds
circular, track, meeting, laps

Question 3

Two persons A and B start from the same point. A walks 19 m South, then 6 m East. B walks 13 m West, then 16 m East. What is the distance between them?
Step-by-step:
1. A's final position: (6, -19)
2. B's final position: (3, 0)
3. Distance = √[(6-3)² + (-19-0)²] = √[3² + -19²] = 19 m
two-persons, relative, distance

Question 4

Two runners start from the same point on a circular track of length 766 m. Their speeds are 12 m/s and 10 m/s. If they run in the same direction, when will they meet again?
Step-by-step:
1. Relative speed (same direction) = |10 - 12| = 2 m/s
2. Time to meet = Track length / Relative speed = 766 / 2 = 383.0 seconds
circular, track, meeting, laps

Question 5

Two persons A and B start from the same point. A walks 10 m South, then 20 m North. B walks 15 m South, then 14 m East, then 10 m East. What is the distance between them?
Step-by-step:
1. A's final position: (0, 10)
2. B's final position: (24, -15)
3. Distance = √[(0-24)² + (10--15)²] = √[-24² + 25²] = 35 m
two-persons, relative, distance

Question 6

A 173 cm tall person casts a 153 cm shadow. A building casts a 462 cm shadow at the same time. How tall is the building?
Step-by-step:
1. Ratio of shadow to height = 153/173 = 0.88
2. For object: Shadow / Height = 0.88
3. Height = Shadow / Ratio = 462 / 0.88 = 522.4 cm
shadow, similar-triangles, ssc

Question 7

A train 261 m long is running at 68 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 68 km/h = 18.9 m/s
2. Time = Length / Speed = 261 / 18.9 = 13.8 seconds
train, platform, pole, ssc

Question 8

Train A at 61 km/h and Train B at 77 km/h start from stations 336 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 = 61 + 77 = 138 km/h
2. Time = Distance / Relative Speed = 336 / 138 = 2.4 hours
relative, meeting, catch-up

Question 9

A person walks 19 m East, then 25 m West, then 19 m East. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 0 m 0
- East-West: 13 m East
2. Displacement = √(13² + 0²) = √169 = 13 m
3. Total distance walked = 63 m
multi-stage, displacement, complex

Question 10

A person walks 20 m West, then 22 m South, then 16 m East, then 15 m North. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: -7 m South
- East-West: -4 m West
2. Displacement = √(-4² + -7²) = √65 = 8 m
3. Total distance walked = 73 m
multi-stage, displacement, complex

Question 11

Car A at 47 km/h and Car B at 53 km/h start from the same point in the same direction. How long will it take for them to be 329 km apart?
Step-by-step:
1. Relative speed when moving in same direction = |53 - 47| = 6 km/h
2. Time = Distance / Relative Speed = 329 / 6 = 54.8 hours
3. The second car will be 329 km ahead after 54.8 hours
relative, meeting, catch-up

Question 12

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 13

A train moves at 56 km/h for 30 minutes. What distance does it cover?
Time = 30 minutes = 0.5 hours
Distance = 56 × 0.5 = 28.0 km
speed, time, basic

Question 14

A train 167 m long is running at 88 km/h. How long will it take to cross a 161 m long platform?
Step-by-step:
1. Speed = 88 km/h = 24.4 m/s
2. Total distance = Train length + Platform length = 167 + 161 = 328 m
3. Time = Distance / Speed = 328 / 24.4 = 13.4 seconds
train, platform, pole, ssc

Question 15

A person travels at 43 km/h for 2 hours and then at 51 km/h for 2 hours. What is the average speed?
Step-by-step:
1. For equal time intervals, Average Speed = (v1 + v2) / 2
2. = (43 + 51) / 2 = 47.0 km/h
average, speed, distance

Question 16

From point X, a person goes 8 m East, then 6 m North. What is the shortest distance from point X?
Step-by-step:
1. The path forms a right triangle
2. Shortest distance = √(8² + 6²) = √100 = 10 m
shortest-path, pythagoras

Question 17

A person travels at 60 km/h for 2 hours and then at 71 km/h for 2 hours. What is the average speed?
Step-by-step:
1. For equal time intervals, Average Speed = (v1 + v2) / 2
2. = (60 + 71) / 2 = 65.5 km/h
average, speed, distance

Question 18

Car A at 45 km/h and Car B at 50 km/h start from the same point in the same direction. How long will it take for them to be 324 km apart?
Step-by-step:
1. Relative speed when moving in same direction = |50 - 45| = 5 km/h
2. Time = Distance / Relative Speed = 324 / 5 = 64.8 hours
3. The second car will be 324 km ahead after 64.8 hours
relative, meeting, catch-up

Question 19

Two persons A and B start from the same point. A walks 17 m South, then 18 m South. B walks 12 m East, then 15 m North, then 6 m South. What is the distance between them?
Step-by-step:
1. A's final position: (0, -35)
2. B's final position: (12, 9)
3. Distance = √[(0-12)² + (-35-9)²] = √[-12² + -44²] = 46 m
two-persons, relative, distance

Question 20

A train 383 m long is running at 71 km/h. How long will it take to cross a 181 m long platform?
Step-by-step:
1. Speed = 71 km/h = 19.7 m/s
2. Total distance = Train length + Platform length = 383 + 181 = 564 m
3. Time = Distance / Speed = 564 / 19.7 = 28.6 seconds
train, platform, pole, ssc
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