Quantitative Aptitude

Time, Speed and Distance

2,165 Questions
All Core formulas and unit conversion 441 Boats and streams effective speed 396 Relative speed, meetings, and overtaking 375 Average speed 362 Early and late arrival 321 Proportional relationships 202 Stoppage time per hour 35 Train and stationary or moving object crossing 17 Races and dead heats 16

Time, Speed and Distance Questions

Multiple choice

A man travels 160 km. in 10 hours . He travels some distance by cycle with the speed of 8 km. / hours and the remaining distance by bike with the speed of 48 km. / hours . Find the distance (in km.) traveled by cycle and bike separately?

  1. 70 , 90

  2. 74 , 86

  3. 64 , 96

  4. 55 , 105

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let cycle distance = c, bike distance = b. Total: c + b = 160. Time equation: c/8 + b/48 = 10. Multiply time equation by 48: 6c + b = 480. Subtracting distance equation: 5c = 320, so c = 64. Then b = 160 - 64 = 96. Cycle: 64 km at 8 km/h takes 8 hours. Bike: 96 km at 48 km/h takes 2 hours. Total time = 10 hours. Option C is correct.

Multiple choice

Avinash walked 12 km to reach the station from his house. Then he boarded in a train and reached his destination. The average speed of the entire journey was 62 kmph and he took a total time of 6 hours. If the average speed of train was 120 kmph, then what is the ratio of walking speed of Avinash to the speed of train?

  1. 1:9

  2. 2:29

  3. 1:30

  4. 4:5

  5. 3:4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total distance = average speed × total time = 62 × 6 = 372 km. Train distance = 372 - 12 = 360 km. Train time = 360/120 = 3 hours. Walking time = 6 - 3 = 3 hours. Walking speed = 12/3 = 4 kmph. Ratio of walking speed to train speed = 4:120 = 1:30. The question tests understanding of average speed formula and weighted averages.

Multiple choice

Find the distance if: Quantity I: A man covers a distance in 15 hours. He covers first half at 12 km/h and second half at 15 km/h. Quantity II: Two buses moves towards each other at a speed of 30 km/h and 40 km/h respectively. When they meet it is found that faster bus covers 30 km more than slower one.

  1. Quantity II < Quantity I

  2. Quantity II > Quantity I

  3. Quantity II ≤ Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity II = Quantity I or relation cannot be established
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Quantity I: Total time = 15 hours. If distance = D, then D/2/12 + D/2/15 = 15, giving D/24 + D/30 = 15. Solving: D(1/24 + 1/30) = 15, D(9/120) = 15, D = 162 km. Quantity II: Relative speed = 70 km/h. Faster covers 30 km more, so time = 30/10 = 3 hours (since difference in speeds is 10 km/h). Total distance = 70 × 3 = 210 km. Quantity II (210) > Quantity I (162).

Multiple choice

Train A leaves from Lucknow to Kanpur. Half an hour later train B leaves for Lucknow from Kanpur. Two hours after A had started, the trains meet. A has covered 50% more distance than train B when they meet. What is the ratio of the speeds of train A to train B?
  1. $9 : 8$
  2. $8 : 9$
  3. $4 : 5$
  4. $5 : 4$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Train A travels for 2 hours. Train B starts 0.5 hours later, so travels for 1.5 hours. When they meet, A covers 50% more distance than B. Distance_A = 1.5 × Distance_B. Since Distance = Speed × Time: Speed_A × 2 = 1.5 × (Speed_B × 1.5). Speed_A × 2 = 2.25 × Speed_B. Speed_A / Speed_B = 2.25 / 2 = 9/8. Therefore ratio is 9:8. Options B, C, and D are incorrect as they don't match this derived ratio.

Multiple choice

A boat covers 20 km in an hour with downstream and covers the same distance in 2 hours with upstream. Then, find the difference between the speed of boat and the speed of current?

  1. 5

  2. 10

  3. 15

  4. 12.5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Downstream speed = distance/time = 20/1 = 20 km/h. Upstream speed = 20/2 = 10 km/h. Boat speed = (downstream + upstream)/2 = (20+10)/2 = 15 km/h. Current speed = (downstream - upstream)/2 = (20-10)/2 = 5 km/h. Difference = 15-5 = 10 km/h. Option A (5) is just the current speed, option C (15) is just the boat speed.

Multiple choice

A boat can travel 28.8 km downstream in 64 minutes. If the speed of the current is 3 km/hr., how much time the boat will take to travel 168 km upstream?

  1. 24 hours

  2. 16 hours

  3. 8 hours

  4. 7 hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Downstream speed = 28.8km / (64/60)hr = 27 km/hr. Boat speed in still water = Downstream speed - Current speed = 27 - 3 = 24 km/hr. Upstream speed = Boat speed - Current = 24 - 3 = 21 km/hr. Time for 168 km upstream = 168/21 = 8 hours. However, the marked answer assumes boat speed calculation from current speed differently.

Multiple choice

Shambhu swims a certain distance upstream in 7 hours, while he returns the same distance downstream in 5 hours. If the speed of the stream is 2 km/hr, then find the speed of Shambhu in still water.

  1. 12 km/hr.

  2. 10 km/hr.

  3. 8 km/hr.

  4. 15 km/hr.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let Shambhu's speed in still water = v km/hr. Upstream speed = v - 2, downstream speed = v + 2. Distance is same, so 7(v - 2) = 5(v + 2). Expanding: 7v - 14 = 5v + 10. Therefore: 2v = 24, giving v = 12 km/hr. This tests the concept of relative speed in stream conditions where the boat's effective speed changes based on direction.

Multiple choice

Akash when going slower by 15 Km/hr, reaches late by 45 hours. If he goes faster by 10 Km/hr from his original speed, he reaches early by 20 hours than the original time. Find the distance he covers.

  1. 8750 km

  2. 9750 km

  3. 1000 km

  4. 3750 km

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let original speed = v km/hr and original time = t hours. Distance d = vt. When v-15, time = t+45: d = (v-15)(t+45). When v+10, time = t-20: d = (v+10)(t-20). Equating and solving: vt = vt + 45v - 15t - 675 and vt = vt - 20v + 10t - 200. This gives v = 30 km/hr and t = 325 hours. Distance = 30 × 325 = 9750 km.

Multiple choice

Sangram goes downstream with a boat to some destination and returns upstream to his original places in 6 hours. If the speed of the boat in the still water and then stream are 12 km/h and 5 km/h respectively, then find the distance of the destination from the starting position.

  1. 25

  2. 26.67

  3. 33

  4. 29.75

  5. 20
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let distance = d km. Downstream speed = 12+5 = 17 km/h. Upstream speed = 12-5 = 7 km/h. Total time = d/17 + d/7 = 6 hours. Solving: d(1/17 + 1/7) = 6, d(24/119) = 6, d = 6 × 119/24 = 29.75 km. Verification: 29.75/17 + 29.75/7 = 1.75 + 4.25 = 6 hours.

Multiple choice

Car A leaves the city at 5 pm and is driven at a speed of 30 km/hr. 3hrs later another car B leaves the city in the same direction as car A. In how much time will car B be 12 km ahead of car A if the speed of car B is 50km/hr ?

  1. 5 hours

  2. 4.2 hours

  3. 8 hours

  4. 5.1 hours

  5. 12 hours
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

कार A 5 बजे 30 किमी/घंटा से निकलती है। 3 घंटे बाद कार B 50 किमी/घंटा से निकलती है। कार A की दूरी = 30 × 3 = 90 किमी। B को A से 12 किमी आगे जाना है, तो B को कुल 90 + 12 = 102 किमी की दूरी तय करनी है। सापेक्ष गति = 50 - 30 = 20 किमी/घंटा। समय = 102 / 20 = 5.1 घंटे। विकल्प D सही है।

Multiple choice

Shatabdi express leaves Patna at 8:00 am for Delhi. At what time will it reach Delhi? I : For the first 100 km it travels at the speed of 250 km per hour and maintains the same speed during the entire journey. II : It has 5 stoppages in between Delhi and Patna. III : Before every stoppages, it covers a same distance of 240 km.

  1. III and (I or II ) are sufficient

  2. Only III is sufficient.

  3. Only I and II together are sufficient.

  4. Only statement I, II, and III together are sufficient.

  5. None of these
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

None of the statements are sufficient to determine the arrival time. Statement I gives speed (250 km/hr) but we don't know total distance. Statement II gives number of stoppages (5) but not duration of each stop. Statement III says 240 km between stoppages, but with 5 stoppages, this only accounts for 5 × 240 = 1200 km, and we don't know: (a) if this covers the full Patna-Delhi distance, (b) the remaining distance after the last stoppage, or (c) stoppage durations. Even combining all three, we cannot determine the total distance or stoppage times to calculate arrival time.

Multiple choice

Two cars A and B, started simultaneously from the same point in opposite directions, car A towards west and car B moves towards East If speed of car B is 45kmph and after 35 minutes they cover the distance 65.5 km , what is the speed of car A?(in Kmph)

  1. 65.65

  2. 67.28

  3. 75

  4. 71.23

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The cars travel in opposite directions, so their distances add. In 35 minutes (which is 35/60 hours), they cover 65.5 km together. Their combined speed is therefore 65.5 divided by (35/60), which equals 112.29 kmph approximately. Since car B travels at 45 kmph, car A's speed must be 112.29 minus 45, which equals 67.29 kmph. Option B (67.28) matches this calculation with minor rounding difference.

Multiple choice

Rubi goes to a multiplex at the speed of 3 km/hr to see a movie and reaches 5 minutes late. If she travels at the speed of 4 Km/hr she reaches 5 minutes early. Then the distance of the multiplex from her starting point is?(in km/h)

  1. 2

  2. 3

  3. 5

  4. 4
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let distance be d km and correct time be t hours. At 3 km/hr: time = d/3, reaching 5 minutes late means t = d/3 - 5/60. At 4 km/hr: time = d/4, reaching 5 minutes early means t = d/4 + 5/60. Equating: d/3 - 1/12 = d/4 + 1/12. Solving: d/3 - d/4 = 1/6, so d/12 = 1/6, giving d = 2 km.

Multiple choice

If I walk at 4 km/hr, I miss the bus by 10 minutes.If I walk at 5 km/hr, I am 5 minutes early. How much do I walk to reach the bus stand?

  1. 3 km

  2. 5 km

  3. 4 km

  4. 6 km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let distance be d km and correct time to reach bus stand be t hours. At 4 km/hr: time taken = d/4 hours, but we miss by 10 minutes, so d/4 = t + 10/60. At 5 km/hr: time taken = d/5 hours, and we're 5 minutes early, so d/5 = t - 5/60. Subtracting: d/4 - d/5 = 15/60 = 1/4, so d/20 = 1/4, giving d = 5 km.

Multiple choice

A truck starts running at the speed of 48km/hr. If the speed of the truck increases 6 km at the end of every hour then what will be the distance covered at the end of 12 hrs from the start of the Journey?

  1. 962

  2. 972

  3. 984

  4. 980
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is an arithmetic progression problem with first term 48 km/hr and common difference 6 km/hr. The distance covered each hour forms the sequence: 48, 54, 60, ... for 12 hours. Using the sum formula S = n/2 × [2a + (n-1)d], we get S = 12/2 × [2×48 + 11×6] = 6 × 162 = 972 km.