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

Two trains started travelling towards each other at the same time from Dehradun and Bhopal. Their respective speed are 60 kmph and 90 kmph. When they meets one train covers 56 km more than other train. Find the distance between second train and Station ?

  1. 300

  2. 550

  3. 280

  4. 650

  5. 400
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Trains travel toward each other with speeds 60 kmph and 90 kmph. Let time until meeting be t hours. Slower train (Dehradun) covers 60t km, faster train (Bhopal) covers 90t km. The difference is 30t = 56 km, so t = 56/30 hours. Distance from Bhopal (second train) to meeting point = 90 × (56/30) = 3 × 56 = 168 km. This would make total distance only 224 km, which doesn't match any option. However, if the question means total distance between stations, then using total distance D and solving properly gives distance from one station as 280 km. Option C (280) matches.

Multiple choice

Time taken by a boat to cover a certain distance in upstream is twice the time taken to cover the same distance in downstream. If speed of the stream is 6 km/hr., what is the speed of boat in still water?

  1. 12 km/hr.

  2. 18 km/hr.

  3. 24 km/hr.

  4. 30 km/hr.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let boat speed = b, stream speed = 6 km/h. Downstream speed = b + 6, upstream = b - 6. Time upstream = 2 × time downstream, so distance/(b-6) = 2 × distance/(b+6). Cancel distance: b + 6 = 2b - 12, giving b = 18 km/h. Option B is correct.

Multiple choice

(\text{A man wants to cover 100 km. But after cover half distance he become tried and cover the remaining distance } \frac{4}{5} \text{th of his actual speed. For that he able to reach in the destination 1hr late. So how much time man will take to cover the distance?})

  1. 8 hours

  2. 9 hours

  3. 10 hours

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

Let actual speed be v km/h and actual time be t hours. Distance = 100 km = v*t. First half (50 km) at speed v takes 50/v hours. Second half at (4/5)v takes 50/(4v/5) = 62.5/v hours. Total time = 50/v + 62.5/v = 112.5/v = t + 1. Since v*t = 100, we have 112.5/v = 100/v + 1, giving 12.5/v = 1, so v = 12.5 km/h. Actual time t = 100/12.5 = 8 hours. Total time with fatigue = 8 + 1 = 9 hours.

Multiple choice

A car is running at the speed of 60 km/hr. It covers a certain distance in 20 minutes. Find the required speed of a bus which covers the distance 20 km more than the distance covered by the car in the same time.
  1. $80 km/hr$
  2. $100 km/hr$
  3. $120 km/hr$
  4. $140 km/hr$
  5. $150 km/hr$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Car's speed is 60 km/hr for 20 minutes (1/3 hour), so distance = 60 × 1/3 = 20 km. Bus must cover 20 + 20 = 40 km in the same 1/3 hour. Required speed = 40 ÷ 1/3 = 120 km/hr. Option B (100) would be too slow for 40 km in 20 min.

Multiple choice

A super fast bus of KSRTC starting from ‘Trivandrum’ and reaches ‘Attingal’ in 45 minutes with an average speed of 40 km/hr. If the speed is increased by 10 km/hr how much time it will take to cover the same distance?

  1. 34 minutes

  2. 36 minutes

  3. 38 minutes

  4. 40 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

With increased speed of 50 km/hr, the bus takes 36 minutes. Distance = Speed × Time = 40 × (45/60) = 30 km. New time = Distance/Speed = 30/50 = 0.6 hours = 36 minutes. When speed increases by 10 km/hr, time decreases proportionally.

Multiple choice

The speed of the boat in still water is 12 kmph. It can travel downstream through 45 kms in 3 hrs. In what time would it cover the same distance upstream?

  1. 3 hours

  2. 4 hours

  3. 5 hours

  4. 7 hours

  5. 9 hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Downstream speed = 45 km / 3 hrs = 15 kmph. Speed of current = downstream speed - still water speed = 15 - 12 = 3 kmph. Upstream speed = still water speed - current = 12 - 3 = 9 kmph. Time upstream = 45 / 9 = 5 hours. Option A (3 hours) incorrectly assumes upstream equals downstream time. Option B (4 hours) is an arithmetic error. Options D (7 hours) and E (9 hours) don't match the calculated upstream speed.

Multiple choice

A person goes along the stream and return in 8 hours. If the speed of person in still water is 4 kmph and that of current is 2kmph. Find the distance covered by person.

  1. 6 km

  2. 10 km

  3. 12 km

  4. 16 km

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

Let the distance be d km. Downstream speed = 4+2 = 6 kmph, upstream speed = 4-2 = 2 kmph. Time downstream = d/6, time upstream = d/2. Total time: d/6 + d/2 = 8 hours. Solving: d/6 + 3d/6 = 4d/6 = 8, so d = 12 km. The person travels 12 km each way, covering 24 km total.

Multiple choice

A goes to his office from his home at the speed of 12 km/hr. If he goes with 5/6 of his usual speed then he will reach late by 20 minutes. Find the distance between his home to office ?

  1. 4 km

  2. 15 km

  3. 20 km

  4. 25 km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Usual speed = 12 km/h. Reduced speed = (5/6) × 12 = 10 km/h. Time ratio is inverse of speed ratio: t_slow/t_fast = 12/10 = 6/5. The 20-minute (1/3 hour) delay equals (6/5 - 1)t_fast = t_fast/5. So t_fast = 5/3 hours. Distance = 12 × 5/3 = 20 km.

Multiple choice

A man covers a distance of 285 km. in 6 hr. First part of the journey he covers at the speed of 40 km/hr. by bus. Second part of the journey he covers at the speed of 55 km./hr. by train . What is the distance covered by train?

  1. 165 km.

  2. 615

  3. 561 km.

  4. 156 km.

  5. 180 km.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let bus distance = d km, train distance = (285-d) km. Bus time = d/40 hours, train time = (285-d)/55 hours. Total: d/40 + (285-d)/55 = 6. Solving: 55d + 40(285-d) = 6×40×55 = 13200. 55d + 11400 - 40d = 13200. 15d = 1800. d = 120 km (bus). Train distance = 285 - 120 = 165 km.

Multiple choice

Two stations A and B are 465 km a part . One train start from A to B at 10:00a.m. at the speed of 65 km/hr another train start from B to A at 11a.m. at the speed of 35km/hr then what time they meet each other at ? दो स्टेशन A तथा B एक दूसरे से 465 किमी. की दूरी पर स्थित है। एक ट्रेन स्टेशन A से B की ओर 65 किमी./घंटा की गति से प्रातः 10 बजे चलती है तथा दूसरी ट्रेन B से A की ओर 35 किमी./घंटा की गति से प्रातः 11 बजे चलती है , दोनों ट्रेने एक-दूसरे से किस समय मिलेंगी?

  1. 2 pm

  2. 3 pm

  3. 4:30 pm

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

Train A starts at 10 am and travels alone for 1 hour until 11 am, covering 65 km. At 11 am, remaining distance = 465 - 65 = 400 km. Both trains now move toward each other at combined speed 65 + 35 = 100 km/hr. Time to meet = 400/100 = 4 hours after 11 am, which is 3 pm. Option A (2 pm) would result from incorrectly calculating remaining distance or relative speed.

Multiple choice

A boat takes 2 hours to travel a distance of 9 km downstream and it takes 6 hours to travel the same distance again the current. The ratio of speed of the boat in still water and that of the current (in km/hr) is- एक नाव धारा के अनुकूल 9 किमी. की दूरी तय करने में 2 घण्टे लेती है और धारा के प्रतिकूल उसी दूरी को तय करने में 6 घण्टे लेती है। नाव की शान्त जल में चाल और धारा की चाल में अनुपात है-

  1. 6 : 9

  2. 2 : 1

  3. 8 : 5

  4. 3 : 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Downstream speed = 9/2 = 4.5 km/hr. Upstream speed = 9/6 = 1.5 km/hr. If boat speed = b and current speed = c: b + c = 4.5 and b - c = 1.5. Solving: b = 3, c = 1.5. Ratio b:c = 3:1.5 = 2:1. Option D (3:1) would be the ratio if current speed was 1 km/hr instead of 1.5 km/hr.

Multiple choice

A person travels with the speed of 4 km/hr and covers the certain distance in 3 hr 45 min. If the person covered the same distance by bicycle with the speed of 16.5 km/h then how much time will he take to cover the same distance. एक व्यक्ति 4 किमी/घं. की चाल से यात्रा करता है और एक निश्चित दूरी को 3 घं. 45 मिनट में तय करता है। यदि वह व्यक्ति उसी दूरी को साइकिल से 16.5 किमी/घं. की चाल से चले तो वह उसी दूरी को तय करने में कितना समय लेगा?

  1. 55.45 min/मिनट

  2. 45.55 min/मिनट

  3. 55.44 min/मिनट

  4. 54.55 min/मिनट
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

First distance = 4 km/hr × 3.75 hr = 15 km. New time = Distance/Speed = 15/16.5 hr = 0.9091 hr × 60 = 54.55 min. Option D matches.

Multiple choice

Speed of a boat is 5 km per hour in still water and the speed of the stream is 3 km per hour. If the boat takes 3 hours to go to a place and come back, the distance of the place is :

  1. 3.75 km

  2. 4 km

  3. 4.8 km

  4. 4.25 km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance be d km. Speed downstream = 5+3 = 8 km/h. Speed upstream = 5-3 = 2 km/h. Time downstream = d/8 hours. Time upstream = d/2 hours. Total time: d/8 + d/2 = 3 hours. Solving: d/8 + 4d/8 = 3, so 5d/8 = 3, giving d = 24/5 = 4.8 km. Option C matches.