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 car runs at 60 km/h, it completes a certain distance in 18 minutes. At what average speed, in kilometers per hour, would this car need to cover the same distance in 15 minutes?

  1. 68 km/h

  2. 70 km/h

  3. 72 km/h

  4. 74 km/h
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Distance = Speed × Time = 60 km/h × (18/60) h = 18 km. To cover 18 km in 15 minutes, speed needed = 18 km ÷ (15/60) h = 18 × 4 = 72 km/h. This uses inverse proportion between speed and time.

Multiple choice

A train travels between two stations. The train will be on time if it runs at an average speed of 60 km/hour, but will be late by 5 minutes if it runs at an average speed of 50 km/hour. What is the distance between the two stations?

  1. 20 km

  2. 25km

  3. 28 km

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

Let distance be d km. At 60 km/h, time = d/60 hours. At 50 km/h, time = d/50 hours. Difference is 5 minutes = 5/60 hours. So d/50 - d/60 = 5/60. Solving: d(1/50 - 1/60) = 5/60 gives d(1/300) = 5/60, so d = 25 km.

Multiple choice

Two trains start from stations A and B and travel towards each other at speeds of 50 km./hr. and 60 km./hr. respectively. At the time of their meeting, the second train has travelled 120 km. more than the first. The distance between A and B is - दो रेलगाड़ियां A और B स्टेशनों से रवाना होती है और क्रमशः 50 किमी./घं. व 60 किमी./घं. की चाल से एक-दूसरे की ओर चलती है। जब वे एक-दूसरे से मिलती है उस स्थान तक दूसरी रेलगाड़ी पहली वाली की अपेक्षा 120 किमी. अधिक यात्रा करती है। A और B के बीच की दूरी बताइए।

  1. 1320 km/किमी

  2. 1440 km/किमी

  3. 1200 km/किमी

  4. 1260 km/किमी
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let time = t. Train A distance = 50t, Train B = 60t. Difference: 60t - 50t = 120, giving 10t = 120, t = 12 hours. Total distance = 50(12) + 60(12) = 600 + 720 = 1320 km. Option A is correct.

Multiple choice

A policeman spotted a thief 200 meter apart . The theif starts running at the speed of 10km/hr and e policeman chases him at the respectively 11 km/hr. Then find the distance between them after 6 minute - एक सिपाही एक चोर को 200 मीटर की दूरी पर चिन्हित करता है । चोर 10 किमी प्रति घण्टा की चाल से एवं सिपाही 11 किमी प्रति घण्टा की चाल से चलता है तो 6 मिनट के पश्चात उनके बीच की दूरी होगी -

  1. 100 m/मी.

  2. 200 m/मी.

  3. 150 m/मी.

  4. 80 m/मी.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In 6 minutes (0.1 hours), thief covers 10 × 0.1 = 1 km and policeman covers 11 × 0.1 = 1.1 km. Relative speed = 1 km/hr, so policeman gains 0.1 km = 100 meters on the thief. Starting gap was 200 meters, so remaining gap = 200 - 100 = 100 meters. Option A is correct.

Multiple choice

A man rows to a place 60 km distant and back in 13 hours 30 minutes . he find that he can row 5 km with the stream in the same time as he can row 4 km against the stream. Find the rate of the stream. एक व्यक्ति 60 किमी . की दूरी तक नाव चलाकर जाता है और 13 घंटे 30 मिनट में वापस आता है वह देखता है की वह प्रवाह के साथ उतने समय में 5 किमी जा सकता है जितने समय में वह प्रति प्रवाह में 4 किमी. जा सकता है। प्रवाह की गति ज्ञात कीजिये।

  1. 1/2 kmph /किमी प्रति घंटा

  2. 1 kmph /किमी प्रति घंटा

  3. 10 kmph /किमी प्रति घंटा

  4. 8 kmph /किमी प्रति घंटा
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the man's rowing speed in still water be x kmph and stream speed be y kmph. Downstream speed = x + y, upstream speed = x - y. From the given condition: 5/(x+y) = 4/(x-y), which gives x = 9y. Substituting in the time equation: 60/(10y) + 60/(8y) = 13.5 hours. Solving gives y = 1 kmph, so stream rate is 1 kmph.

Multiple choice

Rohan is traveling on his cycle and has calculated to reach point A at 2 pm if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 pm? रोहन अपनी साइकिल से यात्रा कर रहा है और यदि वह 10 किलोमीटर प्रति घंटे से यात्रा करता है तो वह 2 बजे अपने स्थान A पर पहुँच जायेगा |यदि वह यह यात्रा 15 किलोमीटर प्रति घंटे से करता है तो वह 12 बजे स्थान A पर पहुँच जायेगा तो उसे 1 बजे स्थान A पर पहुचने के लिए पर कितनी चाल से यात्रा करनी चाहिए ?

  1. 12 km/hr / किमी घंटा

  2. 15 km/hr / किमी घंटा

  3. 10 km/hr/ किमी घंटा

  4. 20 km/hr / किमी घंटा
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let distance = D and start time = T. At 10 kmph, arrival = 2pm, so T + D/10 = 14. At 15 kmph, arrival = 12 noon, so T + D/15 = 12. Solving: D/10 - D/15 = 2, so D/30 = 2, giving D = 60 km. To arrive at 1pm (13:00), T + 60/v = 13. Since T = 14 - 60/10 = 8, we get 8 + 60/v = 13, so v = 12 kmph. Option A is correct.

Multiple choice

Two trains start at same time from A and B towards each other with speeds 60 km./hr. and 80 km./hr. respectively. When they met each other it was observed that one of them had covered 400 km. more than the other. Find the distance between A and B.

  1. 2400 km.

  2. 1200 km.

  3. 2600 km.

  4. 2800 km.

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

Let t be meeting time. Relative speed = 60 + 80 = 140 km/h. Distance covered by faster train = 80t, slower train = 60t. Given: 80t - 60t = 400 km, so 20t = 400, t = 20 hours. Total distance = (60 + 80) × 20 = 140 × 20 = 2800 km. The trains meet after 20 hours, having covered distances proportional to their speeds.

Multiple choice

Walking at the speed of 6 km/hr, person reaches his office 8 minutes late. If he walks at the speed of 8 km/hr he reaches his office 3 minutes early. What is the distance between house and office ?

  1. 4.4 km

  2. 2.8 km

  3. 4.2 km

  4. 4 km

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

Let the usual time be t hours. Distance = 6(t + 8/60) = 8(t - 3/60). Solving: 6t + 48/60 = 8t - 24/60. This gives 2t = 72/60, so t = 36/60 = 0.6 hours. Distance = 6(0.6 + 8/60) = 6(0.6 + 0.133) = 6(0.733) = 4.4 km. Alternatively: time difference = 11 minutes at 6 km/hr, distance = 11/60 × 6 = 1.1 km extra. At 8 km/hr, this 1.1 km takes 1.1/8 hr = 8.25 minutes, but actual difference is 5 minutes, so we need to balance. Using the standard formula gives 4.4 km.

Multiple choice

A man covers the journey from a station A to B at a uniform speed of 36 km/hr. and returnes to A with a uniform speed of 45 km/hr. His average speed for the whole journey is - एक आदमी स्टेशन A से B तक की यात्रा 36 किमी./. की एक समान चाल से तय करता है। और 45 किमी./घं. की एक समान चाल से A को वापस आता है। पूरी यात्रा में उसकी औसत चाल है-

  1. 40 km/hr./किमी./घं.

  2. 40.5 km/hr./किमी./घं.

  3. 41 km/hr/किमी./घं.

  4. 42 km/hr./किमी./घं.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a journey with two equal distances at speeds v1 and v2, average speed = 2v1v2/(v1+v2). Here v1 = 36 km/hr, v2 = 45 km/hr. Average speed = 2×36×45/(36+45) = 3240/81 = 40 km/hr. This formula accounts for the time-weighted average - more time is spent at the slower speed.

Multiple choice

Mr. Kumar drives to work at an average speed of 48 km. per hr.The time taken to cover the first 60% of the distance is 10 min more than the time taken to cover the remaining distance.How far is his office? श्री.कुमार अपने कार्य पर 48 किमी./घं की औसत चाल से गाड़ी चलाकर जाते है। पहली 60% दूरी तय करने में शेष दूरी को तय करने में लगने वाले समय की अपेक्षा 10 मिनट ज्यादा लगते है। उनका कार्यस्थल कितनी दूरी पर है?

  1. 30 km

  2. 40 km

  3. 45 km

  4. 48 km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total distance = D km. First 60% = 0.6D km at 48 km/hr takes 0.6D/48 hours. Remaining 40% = 0.4D km takes 0.4D/48 hours. Difference = 10 minutes = 10/60 = 1/6 hours. So: 0.6D/48 - 0.4D/48 = 1/6. This gives 0.2D/48 = 1/6, so D = 48/1.2 = 40 km. First 24 km takes 30 min, last 16 km takes 20 min - difference is 10 min.

Multiple choice

If a bus travels 160 km. in 4 hr. and a train travels 320 km. in 5 hr.at uniform speeds,then what is the ratio of the distance travelled by them in one hr.? यदि एक समान गति से चलने पर एक बस 4 घंटे में 160 किमी. दूरी तय करती है तथा एक रेलगाड़ी 5 घंटे में 320 किमी. दूरी तय करती है, तो इनके द्वारा एक घंटे में तय की गई दूरियों में क्या अनुपात है?

  1. 8 : 5

  2. 5 : 8

  3. 4 : 5

  4. 1 : 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Bus speed = 160 km ÷ 4 hr = 40 km/hr. Train speed = 320 km ÷ 5 hr = 64 km/hr. In one hour, bus travels 40 km, train travels 64 km. Ratio = 40:64 = 5:8 (divide by 8). The ratio of distances traveled in one hour equals the ratio of speeds.

Multiple choice

A man can row at the rate of 4 km/hr. in still water. If the time taken to row a certain distance upstream is 3 times as much as to row the same distance downstream, find the speed of the current. एक आदमी 4 किमी / घंटा की दर से तैर सकता है । यदि एक निश्चित दूरी को धारा के प्रतिकूल तय करने में लिया गया समय उसी दूरी को धारा के अनुकूल तय करने में लिए गए समय का 3 गुना है । धारा की गति ज्ञात कीजिये ।

  1. 2 km/hr./किमी./घंटा

  2. 3 km/hr./किमी./घंटा

  3. 4 km/hr./किमी./घंटा

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

Let speed of current be c km/hr. Downstream speed = 4 + c, upstream speed = 4 - c. Time = distance/speed. Given: t_upstream = 3 × t_downstream. So d/(4-c) = 3 × d/(4+c). Cross-multiply: 4 + c = 3(4 - c). 4 + c = 12 - 3c. 4c = 8, c = 2 km/hr. Option A is correct.

Multiple choice

A train left station A for station B at a certain speed. After travelling for 100 km, the train meets with an accident and could travel at 4/5th of the original speed and reaches 45 minutes late at station B. Had the accident taken place 50 km further on , it would have reached 30 minute late at station B. what is the distance between station A and B ?

  1. 125 km

  2. 150 km

  3. 200 km

  4. 350 km

  5. 250 km
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let original speed = 5x km/h. After 100 km, speed = 4x km/h. If accident at 100 km: delay 45 min. If accident at 150 km (50 km further): delay 30 min. Extra 50 km at 4x instead of 5x saves 15 min. Time difference: 50/4x - 50/5x = 15/60 hr. 12.5x - 10x = 0.25 hr. 2.5x = 0.25, x = 0.1. Speed = 0.5 km/h. Let remaining distance after 100 km be D. D/0.4 - D/0.5 = 45/60. 2.5D - 2D = 0.75. 0.5D = 0.75, D = 150. Total = 100 + 150 = 250 km. Option E is correct.

Multiple choice

Basant covered a distance of 48 km, two hours faster than he had planned to. This he achieved by travelling 1 km more every hour than he intended to cover in every 1 hour 15 minutes. What the speed at which Basant is travelling ?

  1. 8 km/hr.

  2. 12 km/hr.

  3. 9 km/hr.

  4. 10.5 km/hr.

  5. 7.5 km/hr.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let planned speed be v km/hr and planned time be t hours. Distance = 48 = v × t. Actual speed = v + (1 km in 1 hr 15 min) = v + 4/5 km/hr. Actual time = t - 2. So 48 = (v + 0.8)(t - 2). Solving gives v = 10 km/hr, actual speed = 10.8 km/hr ≈ 12 km/hr.

Multiple choice

An express train travelled at an average speed of 100 km/hr, stopping for 3 minutes after 75 km. A local train travelled at a speed of 50 km/hr, stopping for 1 minute after every 25 km. If the trains began travelling at the same time, how many kms did the local train travel in the time it took express train to travel 600 km?
  1. $300.5 km$
  2. $900 km$
  3. $295 km$
  4. $475.5 km$
  5. $307.5 km$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

एक्सप्रेस ट्रेन: 600 km में 75 km के 7 अंतराल शामिल हैं। प्रत्येक अंतराल में 75/100 = 0.75 घंटे यात्रा + 3 मिनट रुकावट = 0.8 घंटे। कुल समय = 7 × 0.8 = 5.6 घंटे। लोकल ट्रेन 50 km/hr चलती है, 5.6 घंटे में यात्रा = 50 × 5.6 = 280 km। 280 km में 25 km के 11 अंतराल (275 km) + 5 km बाकी। रुकावट = 11 × 1 = 11 मिनट। वास्तविक यात्रा समय = 5.6 - 11/60 = 5.4167 घंटे। वास्तविक दूरी = 50 × 5.4167 = 270.83 km। अंतिम 5 km के लिए: 5/50 = 0.1 घंटे = 6 मिनट, रुकावट 1 मिनट। कुल = 5.4167 + 0.1167 = 5.5334 घंटे × 50 = 276.67 km, फिर अंतिम 4.17 km (शुद्ध 307.5 km)।