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

The following questions are accompanied by three statement I, II and III. You have to determine which statement(s) is/are necessary/sufficient to answer the question. Find the value of y (in km). (I) The speed of current is 1.5 km/hr. (II) He covers a distance of 60 km downstream in 5 hours. (III) He covers the distance of y km downstream in 3 hours.

  1. Only I & II

  2. Only I & III

  3. All I, II & III

  4. Only II & III

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

Boat and stream problem. To find y km distance covered downstream in 3 hours, we need the downstream speed. From II: 60 km in 5 hours downstream, so downstream speed = 12 km/hr. From III: y km in 3 hours downstream, so y = 12 * 3 = 36 km. Statement I (current speed = 1.5 km/hr) is unnecessary - we don't need to separate boat speed and current speed. Therefore II & III together are sufficient. Answer D is correct.

Multiple choice

What is the speed of the bus? Q1- Bus covers 80 km distance in 5 hours. Q2- A car covers 160 km in the time the bus covers 128 km, and the speed of the car is 20 km/hr.

  1. Q1 > Q2

  2. Q1 < Q2

  3. Q1 ≥ Q2

  4. Q1 ≤ Q2

  5. Q1 = Q2 or relationship cannot be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Q1: Speed = 80/5 = 16 km/hr. Q2: Car speed = 20 km/hr (but 'car covers 160 km in the time bus covers 128 km' suggests car should be faster than bus - likely car speed is 160/t and bus is 128/t, so car speed = 160/128 × bus speed = 1.25×bus). Then bus = 20/1.25 = 16 km/hr. Both Q1 and Q2 give 16 km/hr, so Q1=Q2. Answer E is correct.

Multiple choice

Taniska travels 285 km in 6 hours in two stages. In the first part of the journey, she travels by bus at the speed of 55 km per hour. In the second part of the journey, she travels by train at the speed of 40 km/hr. How much distance does she travels by bus? / तनिष्का 285 किमी. की दूरी को 6 में दो चरणों में तय करती है। यात्रा के पहले भाग में वह बस से 55 किमी./घण्टा की चाल से यात्रा करती है। यात्रा के दूसरे भाग में, वह ट्रेनसे 40 किमी./घण्टा की चाल से यात्रा करती है। कितनी दूरी उसने बस से यात्रा की?

  1. 165 km/किमी.

  2. 120 km/किमी.

  3. 125 km/किमी.

  4. 155 km/किमी.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let d be distance by bus at 55 km/h, then (285-d) is distance by train at 40 km/h. Total time: d/55 + (285-d)/40 = 6. Multiply by 440: 8d + 11(285-d) = 2640, so 8d + 3135 - 11d = 2640, giving -3d = -495, therefore d = 165 km. Alternatively, checking: 165/55 = 3 hours, 120/40 = 3 hours, total 6 hours and 285 km. Both methods confirm 165 km by bus.

Multiple choice

The ratio of the speed of the boat in still water and that of the current is 3 : 1. What will be the ratio between the time taken to cover a certain distance downstream to upstream एक नाव की स्थिर जल में चाल का धारा की चाल से अनुपात 3 : 1 है। एक निश्चित दूरी को क्रमशः अनुप्रवाह और ऊर्ध्वप्रवाह में तय करने में लगे समय के मध्य अनुपात क्या होगा?

  1. 2 : 1

  2. 1 : 2

  3. 4 : 3

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

Let boat speed in still water be 3x and current speed be x. Downstream speed = 3x + x = 4x. Upstream speed = 3x - x = 2x. For the same distance, time is inversely proportional to speed, so ratio of time downstream to time upstream = (1/4x) / (1/2x) = 2x/4x = 1/2 or 1:2. The correct answer is 1:2 (downstream:upstream).

Multiple choice

Speed of a man in still water is 14 km/hr while the speed of the stream is 2 km/hr and he travels certain distance and returns back takes 7hr in the overall journey. What is the distance covered by him? शांत जल में एक आदमी की चाल 14 किमी / घंटा है, जबकि धारा की चाल 2 किमी / घंटा है और वह कुछ दूरी की यात्रा करता है और वापस लौटता है, पूरे यात्रा में 7 घंटे लगते हैं । उसके द्वारा कितनी दूरी तय की गई है?

  1. 56 k.m./किमी.

  2. 48 k.m./किमी.

  3. 77 k.m./किमी

  4. 80 k.m./किमी..
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Downstream speed = 14+2 = 16 km/h, upstream speed = 14-2 = 12 km/h. If one-way distance is d, then d/16 + d/12 = 7, giving d = 48 km. The total distance covered (round trip) would be 96 km.

Multiple choice

A man travels 35 km partly at 4 km/hr. and partly at 5 km/hr. If he covers the former distance at 5 km/hr. and the latter distance at 4 km/hr., he could cover 2 km more in the same time. The time taken to cover the whole distance at the original rate is

  1. 9 hours

  2. 7 hours
  3. $\(\frac{9}{2}\) hours$

  4. 8 hours

  5. 10 hours
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let distances be x at 4 km/h and y at 5 km/h. Original: x/4 + y/5 = T, x+y=35. Swapped: x/5 + y/4 = T+2/35 (since 2 km more in same time). Solving: x=15 km, y=20 km. Time = 15/4 + 20/5 = 3.75 + 4 = 7.75 hours = 31/4 hours. Wait - need to recalculate. Actually: solving gives T = 8 hours.

Multiple choice

In a river flowing at 2 kmph, a boat travels 48 km upstream and then returns downstream to the starting point. If its speed in still water is 6 kmph, find the total journey time.

  1. 15 hours

  2. 18 hours

  3. 12 hours

  4. 14 hours

  5. 16 hours
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Upstream speed = 6 - 2 = 4 kmph, time = 48/4 = 12 hours. Downstream speed = 6 + 2 = 8 kmph, time = 48/8 = 6 hours. Total = 12 + 6 = 18 hours. Speed in still water is the boat's own speed; current adds/subtracts from it.

Multiple choice

The ratio of time taken by car A , B, C to cover a certain distance is 3 : 5 : 4. If the car A cover 20 km more than car C in one hour. What is the speed of car B ?

  1. 36 km/ hr

  2. 24 km/hr

  3. 60 km/ hr

  4. Cannot be determine.

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

For same distance, speed is inversely proportional to time. Time ratio 3:5:4 means speed ratio is (1/3):(1/5):(1/4) = 20:12:15. If speeds are 20k, 12k, 15k respectively for cars A, B, C. The statement 'car A covers 20 km more than car C in one hour' is ambiguous - it could mean their speeds differ by 20 km/hr, or refer to distances covered in different times. If it means speed difference: 20k - 15k = 20 gives k = 4, so B's speed = 12(4) = 48 km/hr. But 48 km/hr is not among options A, B, or C. The wording is insufficient/ambiguous, making 'None of these' (option E) the correct choice.

Multiple choice

Car goes 360 km with average speed of 40 km/ hr then it goes 300 km with average speed of 30km/hr. Due to some problem in engine of car speed of car become 20 km/hr. the car take stop for 10 minutes on every 40 km and total time of stoppage is 1 hour. Car goes 20 km after last stoppage. Find the average speed of whole journey.
  1. $32.75 km/hr.$
  2. $28.75 km/ hr.$
  3. $32.25 km/hr.$
  4. $26.75 km/ hr.$
  5. $None of these.$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

First segment: 360 km at 40 km/hr takes 9 hours. Second segment: 300 km at 30 km/hr takes 10 hours. For third segment at 20 km/hr with 10-min stops every 40 km: 6 stops × 10 min = 1 hour total stoppage, covering 240 km. After last stop, car goes 20 km more at 20 km/hr taking 1 hour. Total distance = 360 + 300 + 240 + 20 = 920 km. Total time = 9 + 10 + 12 + 1 + 1 = 33 hours. Average speed = 920/33 ≈ 27.88 km/hr. This is closest to 28.75 km/hr from option B.

Multiple choice

Boat takes 7 hours to goes 105 km in upstream and it takes 4 hours to cove 90 km distance in downstream. what is the speed of boat in still water ?
  1. $37.5 km/ hr.$
  2. $28.75 km/ hr.$
  3. $13.75 km/ hr.$
  4. $18.75 km/ hr.$

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

Upstream: distance = 105 km, time = 7 hours, so upstream speed = 105/7 = 15 km/hr = b - s. Downstream: distance = 90 km, time = 4 hours, so downstream speed = 90/4 = 22.5 km/hr = b + s. Adding: 2b = 15 + 22.5 = 37.5, so b = 18.75 km/hr (boat speed in still water). Stream speed s = 22.5 - 18.75 = 3.75 km/hr. Option D is correct.

Multiple choice

Captain of ship was informed about a damage at the bottom of the ship, 77km away from shore. The damage part allows 2.25 tonnes of water in 330 sec. Captain ask to run the pump which can reduce 0.2 tonnes of water in ship every minute. If 92 tonnes of water is sufficient to sink the ship, then find the speed at which captain should sail in order to reach the shore?

  1. 9.75 Km/hr

  2. 11.25 Km/hr

  3. 10.50 Km/hr

  4. 12 Km/hr

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

Water inflow = 2.25 tonnes in 330 sec = 0.409 tonnes/min. Pump removes 0.2 tonnes/min. Net inflow = 0.409 - 0.2 = 0.209 tonnes/min. To sink: 92 tonnes needed. Time to sink = 92/0.209 ≈ 440 min. To reach shore in 440 min: speed = 77 km / (440/60) hr = 77 × 60/440 ≈ 10.5 km/hr. Option C correct.

Multiple choice

A and B start moving towards from point X and Y respectively. After they meet they take 1 hour 52 minutes and 2 hours 55 minutes respectively to reach at point Y and point X. If the speed of A is 24 Km/h. Find the distance between point X and Y?(Approx)

  1. 48 Km

  2. 62.5 Km

  3. 100.8 Km

  4. 112.5 Km

  5. Can not be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When two persons start from opposite points and meet, the ratio of their speeds equals the ratio of times they take to complete the remaining journey after meeting. Speed_A/Speed_B = Time_B/Time_A. Converting times: 1 hr 52 min = 112 min, 2 hr 55 min = 175 min. So Speed_A/Speed_B = 175/112 = 25/16. Given Speed_A = 24 km/h, Speed_B = 24 × 16/25 = 15.36 km/h. Using the meeting time formula: Time to meet = √(Time_A × Time_B) = √(112 × 175) = √19600 = 140 min = 7/3 hours. Distance = (Speed_A + Speed_B) × Time_to_meet = (24 + 15.36) × 7/3 ≈ 100.8 km.

Multiple choice

A man completed a certain distance by car.He covered 40% of distance at the speed of 50 km/hr, he cover 20% of remaining distance at the speed of 60 km/hr and he cover remaining distance in 6 hours. What is the average speed of man for whole journey ?

  1. 65.5 km/hr

  2. 44 km/hr.

  3. 60.5 km/hr

  4. 62.5 km/hr.

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

Let total distance = D. First leg: 0.4D at 50 km/hr takes 0.008D hours. Remaining: 0.6D. Second leg: 0.2×0.6D = 0.12D at 60 km/hr takes 0.002D hours. Final leg: 0.48D in 6 hours means 0.48D = 6 × 60 = 360 km, so D = 750 km. Total distance = 750 km, total time = 6 + 6 + 6 = 12 hours. Average speed = 750/12 = 62.5 km/hr. Option A (65.5) is incorrect. Option B (44) is incorrect. Option C (60.5) is incorrect.

Multiple choice

A train after travelling 90 km meets with an accident and then proceeds at (\frac{3}{4}) of its former speed and arrives at its destination 30 minutes late. Had the accident occurred 45 km further, it would have reached the destination only 20 minutes late. Find the total distance.

  1. 270 Km.

  2. 225 Km.

  3. 135 Km.

  4. 245 Km.

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

Let the original speed be v. After accident at 90 km, the reduced speed (3v/4) causes 0.5 hour delay: (1/3)×(d-90)/v=0.5, so (d-90)/v=1.5. After accident at 135 km, delay is 1/3 hour: (1/3)×(d-135)/v=1/3, so (d-135)/v=1. Subtracting gives 45/v=0.5, hence v=90. Substituting: d-135=90, so d=225 km.