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

Waking (\frac{3}{4}) of his normal speed, a man is 24 minutes late in reaching his office. The usual time taken by him to cover the distance between his home and office:

  1. 60 minutes

  2. 64 minutes

  3. 68 minutes

  4. 72 minutes
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When walking at 3/4 of normal speed, time becomes 4/3 of usual time. The extra time is (4/3 - 1) × usual time = 24 minutes. So (1/3) × usual time = 24, giving usual time = 72 minutes. Verification: At 3/4 speed, time = 72 × 4/3 = 96 minutes, which is 24 minutes more than usual.

Multiple choice

The speed of a stream is 3 km/hr. and the speed of a man in still water is 5 km/hr. The time taken by the man to swim 52 km downstream is
  1. $8(2/3) hrs.$
  2. $6(1/2) hrs.$
  3. $13 hrs.$
  4. $5(1/5) hrs.$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Downstream speed = Man's speed in still water + Stream speed = 5 + 3 = 8 km/hr. Time = Distance/Speed = 52/8 = 6.5 hours = 6(1/2) hours. When swimming downstream, the stream assists the swimmer, so effective speed is additive.

Multiple choice

The speed of a car increases by 4 kmph after every one hour. If the distance travelled in the first one hour is 32 km, what was the total distance travelled by the car in 11 hours? (in km.)

  1. 572

  2. 584

  3. 564

  4. 612
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial speed = 32 kmph (distance in 1st hour). Speed increases by 4 kmph each hour: 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72. Total distance = sum of this arithmetic progression = 11/2 × (2×32 + 10×4) = 11/2 × 104 = 572 km. Option D (612) would result from using n = 12 instead of 11 hours.

Multiple choice

A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/hr. less, then it would have been taken 3 hours more to cover the same distance. Find the usual speed of the train. एक रेलगाड़ी एक 480 किमी. की दूरी को एक समान चाल से तय करती है | यदि चाल को 8 किमी./घंटा कम कर दी जाय, तो यह उसी दूरी को तय करने में 3 घंटे अधिक लेती है | रेलगाड़ी की मूल चाल ज्ञात कीजिये |

  1. 32

  2. 36

  3. 40

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

Let usual speed = x km/hr. Time at usual speed = 480/x hours. At reduced speed (x-8) km/hr, time = 480/(x-8) hours. Given: 480/(x-8) - 480/x = 3. Solving: 480x - 480(x-8) = 3x(x-8). 480x - 480x + 3840 = 3x² - 24x. 3x² - 24x - 3840 = 0. Dividing by 3: x² - 8x - 1280 = 0. Using quadratic formula: x = [8 ± √(64 + 5120)]/2 = [8 ± √5184]/2 = [8 ± 72]/2. x = 40 or x = -32 (reject negative). Speed = 40 km/hr. This matches option C.

Multiple choice

A man starts walking and covers 50 m in 1 minute, 90 m in 2 minutes, 130 m in 3 minutes and so on. Find the total distance covered by the man in 15 minutes. If the speed of the man is the same in the first and last minute and constant in the rest of the time, then find the distance covered by the person in 15 minutes.
  1. $520 m$
  2. $620 m$
  3. $720 m$
  4. $750 m$

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The distances form an AP: 50, 90, 130, ... with first term a = 50 and common difference d = 40. This is distance covered BY THE END of each minute. Sum of 15 terms = 15/2 × [2(50) + (15-1)(40)] = 15/2 × [100 + 560] = 15/2 × 660 = 4950 m. If the problem asks for distance covered IN 15 minutes (not total), we need the 15th term alone: 50 + 14×40 = 610 m. The closest option is B (620 m). Options A (520), C (720), and D (750) don't match.

Multiple choice

A man goes a distance of 2304 km down stream in x hours.and returns back a certain distance upstream the same time interval. If the speed of the current is 4 km/hr and speed of the boat is 15 times the speed of the current. Find the distance covered by the boat up in number of hours mentioned above.

  1. 2010

  2. 2012

  3. 2014

  4. Cannot be determinded

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

Speed of current = 4 km/hr, speed of boat = 15 × 4 = 60 km/hr. Downstream speed = 60 + 4 = 64 km/hr. Time for 2304 km downstream = 2304/64 = 36 hours. Upstream speed = 60 - 4 = 56 km/hr. Distance upstream in 36 hours = 56 × 36 = 2016 km. None of A (2010), B (2012), or C (2014) match 2016 km.

Multiple choice

A train covers a distance of 3584 km in 2 days 8 hours. If it covers 1440 km on the first day and 1608 km on the seocnd day, by how much does the average speed of the train for the remaining part of the journey differ from that for the entire journey? एक ट्रेन 3584 किमी. की दूरी को 2 दिन 8 घंटे में तय करती है | यदि यह 1440 किमी. की दूरी पहले दिन और 1608 किमी. की दूरी दूसरे दिन तय करती है, ट्रेन की औसत चाल शेष दूरी को तय करने में पूरी दूरी से कितना भिन्न होगी ?

  1. 1

  2. 2

  3. 3

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

Total time = 2 days 8 hours = 56 hours. Total distance = 3584 km. Average speed for entire journey = 3584/56 = 64 km/hr. Remaining distance after 2 days = 3584 - 1440 - 1608 = 536 km covered in 8 hours, so average speed = 536/8 = 67 km/hr. Difference = 67 - 64 = 3 km/hr.

Multiple choice

A boat can cover certain distance in downstream in 1 hr. and it takes 1½ hr. to cover same distance in upstream. If speed of the stream is 3 kmph, then what will be time taken by the boat to travel a distance of 75 km in still water? एक नाव अनुप्रवाह में निश्चित दूरी को 1 घंटे में तय करती है और यह उसी दूरी को ऊर्ध्वप्रवाह में तय करने के लिए 1½ घंटे लेती है | यदि धारा की चाल 3 किमी./घंटा है, तो शांत जल में नाव को 75 किमी. की दूरी तय करने में लिया गया समय क्या है?

  1. 5.5 hours/घंटे

  2. 4 hours/घंटे

  3. 3 hours/घंटे

  4. 5 hours/घंटे
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let boat speed in still water = b kmph, stream speed = 3 kmph. Downstream speed = b + 3, upstream speed = b - 3. If distance is D, then D/(b+3) = 1 hour, and D/(b-3) = 1.5 hours. So D = b + 3 and D = 1.5(b - 3). Equating: b + 3 = 1.5b - 4.5, so 0.5b = 7.5, b = 15 kmph. Time for 75 km in still water = 75/15 = 5 hours. The key is to find the boat's speed in still water first using the ratio of downstream and upstream times.

Multiple choice

A cyclist in a fog passed a man running at the rate of 6 km/hr. in the same direction.He could see the cyclist for 5 min.and it was visible to him upto a distance of 100 m. What was the speed of the cyslist ? कोहरे में एक साइकिल सवार ,उसी समान दिशा में 6 किमी./घं.की चाल से दौड़ रहे एक आदमी को पार करता है। वह साइकिल सवार को 5 मिनट के लिए देखता है और यदि उसके लिए 100 मी. तक की दूरी दृश्य थी, तो साइकिल सवार की चाल क्या थी?

  1. 7.20 km./hr./किमी./घं

  2. 8.4 km./hr./किमी./घं

  3. 8.5 km./hr./किमी./घं

  4. 9 km./hr./ किमी./घं
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Relative speed between cyclist and runner = 100 m / 5 min = 100/300 m/s = 1/3 m/s = 1.2 km/hr. Cyclist speed = Runner speed + Relative speed = 6 + 1.2 = 7.2 km/hr.

Multiple choice

A boat goes 40 km down stream in one hour and the same distance upstream in two hours. The speed of the boat in still water is - एक नाव धारा के विपरीत 40 किमी की दूरी एक घण्टे में तथा उतनी ही दूरी धारा की दिशा में दो घंटे में तय करती है। शांत जल में नाव की चाल क्या है।

  1. 30 kmph / किमी./घण्टा

  2. 25 kmph / किमी./घण्टा

  3. 20 kmph / किमी./घण्टा

  4. 15 kmph / किमी./घण्टा
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Downstream speed (boat + current) = 40 km/h since 40 km is covered in 1 hour. Upstream speed (boat - current) = 20 km/h since 40 km takes 2 hours. Adding these equations: 2 × boat speed = 60, so boat speed = 30 km/h.

Multiple choice

A boat running downstream covers a distance of 30 km in 2 hours. While coming back the boat takes 6 hours to cover the same distance. If the speed of the current is half of that of the boat, then what is the speed of the boat in kmph?

  1. 15 kmph

  2. 5 kmph

  3. 10 kmph

  4. 12 kmph
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Downstream speed = 30/2 = 15 kmph. Upstream speed = 30/6 = 5 kmph. Let boat speed = b, current speed = c. Downstream: b + c = 15. Upstream: b - c = 5. Given c = b/2 (current is half of boat speed). Substituting: b + b/2 = 15 gives 3b/2 = 15, so b = 10 kmph. Check: c = 5 kmph, which satisfies both equations. Option C is correct.

Multiple choice

On a journey across Mumbai, a train averages 50 km per hour for 50% of the distance, 40 km per hour for 40% of it and 20 km per hour for the remaining. The average speed (in km/hour) for the whole journey is:

  1. 42

  2. 40

  3. 35

  4. 45
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average speed = Total distance / Total time. Let total distance = D. Time for each part: first 50% at 50 kmph = 0.5D/50 = D/100 hours. Next 40% at 40 kmph = 0.4D/40 = D/100 hours. Remaining 10% at 20 kmph = 0.1D/20 = D/200 hours. Total time = D/100 + D/100 + D/200 = 5D/200 = D/40. Average speed = D / (D/40) = 40 kmph. Option B is correct. Option A (42) and D (45) incorrectly weight the speeds.

Multiple choice

One-third of a certain journey was covered at the speed of 20 km./hr., one-fourth at 30 km./hr. and the rest at the speed of 50 km./hr. The average speed per hour for the whole journey is - एक यात्रा का एक तिहाई 20 किमी./घं. की चाल से, एक चौथाई 30 किमी./घं. की चाल से और शेष 50 किमी./घं. की चाल से तय की जाती है। पूरी यात्रा में औसत चाल प्रति घंटा क्या है?

  1. 33.33

  2. 30

  3. 28

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

For average speed, we need total distance divided by total time, not the average of speeds. Let total distance be 12 units (LCM of 3, 4, and remaining 5). Time taken: 4 units at 20 km/h = 0.2h, 3 units at 30 km/h = 0.1h, 5 units at 50 km/h = 0.1h. Total time = 0.4h, so average speed = 12/0.4 = 30 km/h. Option A (33.33) incorrectly averages the speeds.