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 boat running downstream covers a distance of 24 km in 2 hours while for covering the same distance upstream it takes 4 hours. what is the speed of the boat in still water? एक नाव को 24 किमी. धारा की अनुकूल दिशा में जाने 2 घंटे लगते है, परन्तु धारा की प्रतिकुल दिशा में उतनी ही दूरी के लिये 4 घंटे लगते है। स्थिर पानी में नाव की चाल क्या है?

  1. 9 km/hr/किमी./घंटे

  2. 12 km/hr/किमी./घंटे

  3. 10 km/hr/किमी./घंटे

  4. 8 km/hr/किमी./घंटे
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Downstream speed = 24/2 = 12 km/hr. Upstream speed = 24/4 = 6 km/hr. Speed of boat in still water = (downstream + upstream)/2 = (12 + 6)/2 = 9 km/hr. Option A is correct.

Multiple choice

A man has to be at a certain place at a certain time. The finds that he shall be 20 minutes late if he walk at 3 km./hr. speed and 10 minutes earlier if he walks at a speed of 4 km./hr. The distance he has to walk is - एक व्यक्ति को एक निश्चित स्थान पर नियत समय के अनुसार पहुँचना है। उसे पता चलता है कि यदि वह 3 किमी./घं. की गति से चले, तो वह 20 मिनट देरी से वहाँ पहुँचेगा, किन्तु यदि वह 4 किमी./घं. की गति से चले, तो 10 मिनट पहले पहुँच जायेगा। तो उस व्यक्ति को कितनी दूर चलना है?

  1. 24 km./किमी.

  2. 12.5 km./किमी.

  3. 10 km./किमी.

  4. 06 km./किमी.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let distance = d km and scheduled time = t hours. Time at 3 km/hr = d/3, time at 4 km/hr = d/4. Time difference = 20 + 10 = 30 minutes = 0.5 hours. So d/3 - d/4 = 0.5, which gives d/12 = 0.5, therefore d = 6 km.

Multiple choice

A motorboat takes 2 hours to travel a distance of 9 km. down the current and it takes 6 hours to travel the same distance against the current. What is the speed of the boat in still water in km./hr.? एक मोटरबोट बहाव की दिशा में 9 किमी. की दूरी तय करने में 2 घंटे लेती है और बहाव की विपरीत दिशा में वही दूरी तय करने में 6 घंटे लेती है। स्थिर पानी में बोट की चाल किमी./घं. में कितनी है?

  1. 3

  2. 2

  3. 1.5

  4. 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Downstream speed = 9/2 = 4.5 km/hr, upstream speed = 9/6 = 1.5 km/hr. Let boat speed be b and current speed be c. Then b + c = 4.5 and b - c = 1.5. Adding these equations gives 2b = 6, so b = 3 km/hr. This is the speed of the boat in still water.

Multiple choice

Walking at a speed of 5 km/hr, a boy reaches his office 6 minutes late. Walking at 6 km/hr, he reaches there 2 minutes early. The distance of his office is- 5 किमी,/घंटा की चाल से चलता हुआ एक लड़का अपने ऑफिस 6 मिनट देरी से पहुँचता है | 6 किमी./घंटा की चाल से चलता हुआ वह उसी स्थान पर 2 मिनट पहले पहुँचता है | उसके ऑफिस की दूरी है -

  1. 3 km./किमी.

  2. 4 km./किमी.

  3. 3.5 km./किमी.

  4. 2 km./किमी.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Time difference between late and early arrival is 6+2=8 minutes. At 5 km/hr and 6 km/hr, let distance=d km. d/5-d/6=8/60 hours. Solving gives d=4 km.

Multiple choice

The distance between the two towns is 800 km. A car starts from the first town with a speed of 30 km./hr. At the same time, another car starts from the second town with a speed of 50 km./hr. The distance (in km.) of the point, where they meet, from the first town is? दो नगरों के बीच की दूरी 800 किमी. है। एक कार पहले नगर से 30 किमी./घं की चाल से चलती है और उसी समय दूसरे नगर से दूसरी कार 50 किमी./घं की चाल से चलती है, तो पहले नगर से दूरी ज्ञात कीजिए जहाँ पर वे मिलती है। (किमी. में)

  1. 200

  2. 300

  3. 350

  4. 400
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cars move toward each other at combined speed 30 + 50 = 80 km/h. Time to meet = 800/80 = 10 hours. Distance from first town = 30 × 10 = 300 km. Verification: second car travels 50 × 10 = 500 km, total = 300 + 500 = 800 km. Correct.

Multiple choice

A man can swim 3 km/hr. in still water of the velocity of the stream is 2 km/hr, the time taken by him to swim to a place 10 km upstream and back is- शांत जल में एक व्यक्ति की गति 2 किमी /घंटे हैं, तो धारा के प्रतिकूल 10 किमी तथा वापस आने में उसे कितने समय लगेगा?

  1. 10

  2. 12

  3. 15

  4. 16
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Wait, question has error: "swim 3 km/hr in still water" but says "velocity of stream is 2 km/hr". This is contradictory - it says swim speed is 3 km/hr, then says still water speed is 2 km/hr. Assuming swim speed = 3 km/hr (from first statement) and stream = 2 km/hr. Upstream speed = 3 - 2 = 1 km/hr, Downstream = 3 + 2 = 5 km/hr. Time = 10/1 + 10/5 = 10 + 2 = 12 hours.

Multiple choice

A boy travels a distance of 8 km at the rate of 4 km per hour, 6km at the rate of 3 km per hour and 4 km at the rate of 2 km per hour.What is the average speed for the entire journey? एक लड़का 8 किमी. की दूरी 4 किमी प्रति घंटा की दर से, 6 किमी की दूरी 3 किमी प्रति घंटा की दर से और 4 किमी की दूरी 2 किमी प्रति घंटा की दर से तय करता है। पूरी यात्रा की औसत चाल क्या है?

  1. 2 kmph/2 किमी प्रति घंटा

  2. 3 kmph/3 किमी प्रति घंटा

  3. 4 kmph/4 किमी प्रति घंटा

  4. 6 kmph/6 किमी प्रति घंटा
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total distance = 8 + 6 + 4 = 18 km. Total time = 8/4 + 6/3 + 4/2 = 2 + 2 + 2 = 6 hours. Average speed = 18/6 = 3 km/h. Option A (2 km/h) is arithmetic mean of speeds, which is incorrect for average speed. Option C (4 km/h) is the speed of the first segment only. Option D (6 km/h) is double the correct answer.

Multiple choice

The ratio of the speed of a bus and a train is 15 : 27 respectively. A car can cover 720 km in 9 hrs and the speed of the bus is three-fourth of the car speed. Find the distance travelled by the train in 7 hours?

  1. 720

  2. 736

  3. 744

  4. 756

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

Car speed = 720/9 = 80 km/hr. Bus speed = 3/4 of car = 60 km/hr. Given bus:train = 15:27, so train speed = 60 × 27/15 = 108 km/hr. Distance by train in 7 hours = 108 × 7 = 756 km.

Multiple choice

A boat covers a distance of 40 km in 8 hours against the stream and covers a distance of 36 km in 6 hours with the stream. Find the speed of the boat in still water.

  1. 6.5 km/hr

  2. 6 km/hr.

  3. 5 km/hr.

  4. 5.5 km/hr.

  5. 4 km/hr.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Against stream: speed = 40/8 = 5 km/hr (boat - stream). With stream: speed = 36/6 = 6 km/hr (boat + stream). Adding: 2 × boat = 11, so boat = 5.5 km/hr. Option B (6 km/hr) is the downstream speed, not still water speed.

Multiple choice

Train A takes 6 hours more than train B to cover a distance of 600 km. If the speed of train A is doubled, it takes 2 hours less than train B. What is the speed of train B?
  1. $50 km/hr.$
  2. $60 km/hr.$
  3. $70 km/hr.$
  4. $75 km/hr.$
  5. $80 km/hr.$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let speed of B = v km/hr, speed of A = u km/hr. Distance = 600 km. Time A = 600/u, Time B = 600/v. First condition: 600/u = 600/v + 6. When A's speed doubles: 600/(2u) = 600/v - 2. Solving gives v = 60 km/hr. From equation: 600/v = 600/u - 6. Substituting v = 60: 10 = 600/u - 6, so u = 37.5. Verify: 600/37.5 = 16 hrs, 600/60 = 10 hrs. Difference is 6 hours ✓ When A doubles: 600/75 = 8 hrs, which is 2 hrs less than B ✓

Multiple choice

A man rows a boat 3 hours downstream and 3 hours upstream. Find speed of the boat in still water, if he covers a total distance of 18 km.

  1. 2 km/hr.

  2. 3 km/hr.

  3. 4 km/hr.

  4. 4.5 km/hr.

  5. 5 km/hr.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total distance = 18 km covered in 3 hours downstream + 3 hours upstream. Speed = distance/time = 18/6 = 3 km/hr. This average speed equals the speed in still water since the time spent going upstream and downstream is equal.

Multiple choice

A man covers a distance of 1440 km in 36 hours down the stream. If the speed of the current is (\frac{1}{7}) of the speed of the boat's speed. Find the speed of the stream.

  1. 40 km/hr

  2. 12 km/hr

  3. 7.5 km/hr

  4. 5 km/hr

  5. 2.5 km/hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Downstream speed = 1440/36 = 40 km/hr. Boat speed + stream speed = 40. Given stream = boat/7, let boat = 7x, stream = x. 7x + x = 40, so 8x = 40, x = 5. Stream speed is 5 km/hr. Option D matches.

Multiple choice

A man covers a certain distance by bus, moving at a speed of 60 km./hr. and he returns to the starting point by train, running at the speed of 100 km./hr. Find the average speed of the whole journey? एक आदमी एक निश्चित दूरी बस से 60 किमी./घं.. की चाल से तय करता है और वह वापस प्रारम्भिक बिन्दु पर रेलगाड़ी से 100 किमी./घं. की चाल से आता है। पूरी यात्रा में उसकी औसत चाल ज्ञात कीजिए।

  1. 60 km./hr./किमी./घं.

  2. 65 km./hr./किमी./घं.

  3. 70 km./hr./किमी./घं.

  4. 75 km./hr./किमी./घं.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When distances are equal, average speed = 2ab/(a+b) where a and b are the two speeds. Here: 2×60×100/(60+100) = 12000/160 = 75 km/hr. The average is always less than the arithmetic mean (80) because more time is spent at the slower speed.