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

If A can row 15km downstream in 12 minutes and his rowing speed in still water is 56kmph, then how much distance can he cover upstream in 20 minutes?

  1. 9km

  2. 24km

  3. 10km

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

Downstream distance = 15km in 12 minutes = 75kmph. Downstream speed = rowing speed + current, so current = 75 - 56 = 19kmph. Upstream speed = 56 - 19 = 37kmph. In 20 minutes (1/3 hour), upstream distance = 37 × (1/3) = 12.33km, which is not among options A-C. Hence D is correct.

Multiple choice

A passenger train 150m long is travelling with a speed of 36 km/hr. If a man is cycling in the direction of the train at 9 km/hr., the time taken by the train to pass the man is

  1. 10 sec

  2. 15 sec

  3. 18 sec

  4. 20 sec
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The train's length must cover the entire distance relative to the man. Relative speed = (36-9) kmph = 27 kmph = 27 × 5/18 = 7.5 m/s. Time = Distance/Relative Speed = 150m/7.5 m/s = 20 seconds. The man is moving in the same direction, so we subtract speeds.

Multiple choice

A man travelled a certain distance by train at the rate of 50 km/hr and come back by running at average speed of 8 km/hr. The journey took 2 hours 54 min. What distance did he travelled by train?

  1. 20 km

  2. 24 km

  3. 16 km

  4. 32 km
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let distance by train = d km. Time by train = d/50 hours. Time running back = d/8 hours. Total time = 2 hours 54 min = 2.9 hours = 29/10 hours. Therefore: d/50 + d/8 = 29/10. Multiplying by 200: 4d + 25d = 580, so 29d = 580, hence d = 20 km. Verify: 20/50 + 20/8 = 0.4 + 2.5 = 2.9 hours = 2 hours 54 minutes.

Multiple choice

A train travels a distance of 384 km at an average speed of 160 km/h from station A to station B. It then travels back to A taking 5 h 36 min. Find the average speed of the train on the return journey to A. एक ट्रेन स्टेशन A से स्टेशन B तक 384 किमी. की एक दूरी को 160 किमी./घंटा की औसत चाल से तय करती है | यह फिर वापस A की ओर यात्रा की दूरी को 5 घंटे 36 मिनट में तय करती है | वापस A की ओर यात्रा करने में ट्रेन की औसत चाल ज्ञात कीजिये |

  1. 144 kmph 144 किमी./घंटा

  2. 72 kmph 72 किमी./घंटा

  3. 40 kmph 40 किमी./घंटा

  4. 120 kmph 120 किमी./घंटा

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

Distance = 384 km. Return time = 5h 36min = 5.6 hours. Return speed = Distance/Time = 384/5.6 = 68.57 km/h. The options (144, 72, 40, 120 km/h) don't include the correct answer. Option E (None of these) is correct.

Multiple choice

A man comes out of his house for office. When he goes by 15 km / hr then reaches 5 minutes before time. But when he goes at a speed of 10 km per hour for the office he reaches 20 minutes late. Find the distance ( in km) between house to office? एक आदमी अपने घर से ऑफिस के लिए निकलता है| जब वह 15 किमी प्रति घंटा की रफ़्तार से जाता है तो समय से 5 मिनट पहले पहुच जाता है| परन्तु जब वह 10 किमी प्रति घंटा की रफ़्तार से जाता है तो ऑफिस 20 मिनट लेट पहुचता है| घर से ऑफिस के बीच की दूरी (किमी में) ज्ञात कीजिये?

  1. 25

  2. 12

  3. 12.5

  4. 18

  5. 15
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance = d km and correct time = t hours. At 15 km/h: d/15 = t - 5/60 (5 minutes early). At 10 km/h: d/10 = t + 20/60 (20 minutes late). Subtracting: d/10 - d/15 = 25/60 = 5/12 hours. d/30 = 5/12. d = 150/12 = 12.5 km. The distance between house and office is 12.5 km.

Multiple choice

A boat takes 6 hours to travel certain distance against the stream and comes back to the starting point. If the speed of boat in still water is 4 km/hr. What is the distance between the two points? एक नाव धारा के विरूद्ध एक निश्चित दूरी जाकर प्रारंभिक बिन्दु तक आने में 6 घण्टे लेता है। यदि नाव की चाल शांत जल में 4 किमी./घण्टा है। दोनों बिन्दु के बीच की दूरी क्या है?

  1. 10 km. 10 किमी.

  2. 8 km. 8 किमी.

  3. 7 km. 7 किमी.

  4. 6 km. 6 किमी.

  5. Cannot be determined निर्धारित नहीं किया जा सकता है।
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let stream speed be s km/hr. Distance = d. Total time = d/(4-s) + d/(4+s) = 6. Solving gives d = 12(4-s^2) km. Since s is unknown but must be less than 4 (otherwise boat cannot go upstream), there are multiple possible (s,d) pairs. Without additional information about the stream, distance cannot be uniquely determined.

Multiple choice

A pilot flies an aircraft at a certain speed for a distance of 1600 km. He could have saved 40 min by increasing the average speed of the plane by 80 km/h. Find the average speed of the aircraft. एक पायलट 1600 किमी की दूरी के लिए एक निश्चित गति से एक विमान को उड़ाता है। वह विमान की औसत गति 80 किमी / घंटा बढ़ाकर 40 मिनट बचा सकता था। विमान की औसत गति ज्ञात कीजिए।

  1. 360

  2. 380

  3. 400

  4. 480

  5. None of these इनमे से कोई नही|
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let original speed be v km/h. Original time = 1600/v hours. New speed = (v + 80) km/h. New time = 1600/(v + 80) hours. Time saved = 40 minutes = 2/3 hour. So 1600/v - 1600/(v + 80) = 2/3. Solving: 1600(v + 80 - v)/[v(v + 80)] = 2/3, which gives 128000/[v(v + 80)] = 2/3, or v(v + 80) = 192000. Solving v^2 + 80v - 192000 = 0 gives v = 400 or v = -480. Since speed is positive, v = 400 km/h.

Multiple choice

A trader covers four successive 6 km stretches at speeds of 25 kmph , 50 kmph , 75 kmph , and 150 kmph respectively. Its average speed over this distance is

  1. 25 kmph

  2. 50 kmph

  3. 75 kmph

  4. 150 kmph
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average speed = total distance / total time. Total distance = 24 km. Total time = 6/25 + 6/50 + 6/75 + 6/150 = 6(1/25+1/50+1/75+1/150) = 6(6/150+3/150+2/150+1/150) = 6(12/150) = 72/150 hr. Speed = 24/(72/150) = 50 km/h. This is the harmonic mean of 25, 50, 75, 150 for equal distances. Option C (75) is a distractor - the arithmetic mean of extremes.

Multiple choice

The ratio of speed of two railway locomotives is 5: 4. If they run on parallel tracks in one direction and initially the low speed engine was 8 km ahead of the high speed engine, how much distance will the fast moving engine have to travel to overtake the low speed engine? दो रेलवे इंजनों की चाल का अनुपात 5: 4 है| यदि वे एक दिशा में समान्तर पटरियों पर चलतें हैं और आरम्भ में कम चाल वाला इंजन तेज चाल वाले इंजन से 8 किमी आगे था, तो तेज चाल वाले इंजन को कम चाल वाले इंजन से आगे निकलने के लिए कितनी दूरी तय करनी पड़ेगी?

  1. 48

  2. 36

  3. 40

  4. 32

  5. None of these इनमे से कोई नही|
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speeds be 5x and 4x km/hr. Relative speed = 5x - 4x = x km/hr. Distance to catch up = 8 km. Time = 8/x hours. Distance fast train travels = speed × time = 5x × (8/x) = 40 km.

Multiple choice

A car covers its journey at the speed 60 km/hr. in 15 hours. If the same distance is to be covered in 9 hours, by how much the speed of car will have to increase? एक कार 60 किमी / घंटा की गति से एक यात्रा को 15 घंटे में तय करती है। यदि समान दूरी को 9 घंटो में तय किया जाये तो गति कितनी बढ़ानी होगी ?

  1. 60 km./hr. 60 किमी / घंटा

  2. 50 km./hr. 50 किमी / घंटा

  3. 40 km./hr. 40 किमी / घंटा

  4. 30 km./hr. 30 किमी / घंटा

  5. 20 km./hr. 20 किमी / घंटा
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Distance = 60 × 15 = 900 km. New speed = 900/9 = 100 km/hr. Increase needed = 100 - 60 = 40 km/hr. Option A (60) incorrectly doubles the original speed instead of finding the difference.

Multiple choice

A man can row a certain distance downstream in 12 hour and return the same distance in 18 hour. If the speed of a man in still water is 12 kmph, Find the speed of the stream.V एक आदमी 12 घंटे में एक निश्चित दूरी बहाव की दिशा में जा सकता है और 18 घंटे में समान दूरी वापस आ सकता हैं। यदि आदमी की शांत जल में गति 12 किमी प्रति घंटा है, तो धारा की गति ज्ञात कीजिये।

  1. 2.1 kmph 2.1 किमी/घंटा

  2. 1.5 kmph 1.5 किमी/घंटा

  3. 4.4 kmph 4.4 किमी/घंटा

  4. 2.4 kmph 2.4 किमी/घंटा

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

Let boat speed = 12 kmph (still water), stream speed = s. Downstream speed = 12+s, upstream = 12-s. Distance same, so (12+s)×12 = (12-s)×18. Solving: 144 + 12s = 216 - 18s, so 30s = 72, s = 2.4 kmph. Verification: Downstream speed = 14.4 kmph, distance = 172.8 km. Upstream speed = 9.6 kmph, time = 172.8/9.6 = 18 hours. Answer D is correct.

Multiple choice

Sanju covers 20 km distance with a speed of 5 km/h, then he covers the next 15 km with a speed of 3 km/h and the last 10 km is covered by him with a speed of 2 km/h. Find out his average speed (in km/hr) for the whole journey. (Approx) संजू ने 5 किमी / घंटा की गति के साथ 20 किमी की दूरी तय की, फिर वह अगले 15 किलोमीटर की दूरी 3 किमी / घंटा की रफ्तार से तय करता है और आखिरी 10 किमी की दूरी 2 किमी / घंटा की रफ्तार से तय की जाती है। पूरी यात्रा के दौरान उसकी औसत गति (किमी / घंटा) में ज्ञात कीजिये। (लगभग)

  1. 4.28

  2. 5.15

  3. 2.96

  4. 3.21

  5. 3.67
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total distance = 20+15+10 = 45 km. Time for each leg: 20/5=4 hrs, 15/3=5 hrs, 10/2=5 hrs. Total time = 14 hrs. Average speed = Total distance/Total time = 45/14 ≈ 3.21 km/h. This matches option D.

Multiple choice

Speed of a man in still water is 15 kmph ,while river is flowing with a speed of 3 kmph and time taken to cover a certain distance upstream is 3 hours more than time taken to cover the same distance downstream . Find the distance. पानी में एक व्यक्ति की गति 15 किमी प्रति घंटे है, जबकि नदी 3 किमी प्रति घंटे की रफ्तार से बह रही है और एक दूरी को तय करने में उर्धप्रवाह में लगा समय अनुप्रवाह में लगे समय से 3 घंटे अधिक है, कुल दूरी ज्ञात कीजिये ।

  1. 115 Km 115 किमी

  2. 96 Km 96 किमी

  3. 108 Km 108 किमी

  4. 72 Km 72 किमी

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

Speed in still water = 15 kmph, river speed = 3 kmph. Downstream speed = 15 + 3 = 18 kmph. Upstream speed = 15 - 3 = 12 kmph. Let distance be d. Time downstream = d/18, time upstream = d/12. Given: d/12 - d/18 = 3 hours. Solving: d(1/12 - 1/18) = 3, d(1/36) = 3, d = 108 km.