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

A ship moves at a speed of 32 km/h in still water. It goes 55 km in upstream in 2 hours 45 minutes. How much time will it take to cover the same distance downstream?

  1. 1H 45 min

  2. 2H 25 min

  3. 1H 15 min

  4. 2 H 45 min
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Upstream speed = 55 km / (2h 45m) = 55/2.75 = 20 kmph. Stream speed = 32 - 20 = 12 kmph. Downstream speed = 32 + 12 = 44 kmph. Time downstream = 55/44 = 1.25 hours = 1 hour 15 minutes. The relationship between still water speed, stream speed and direction is key.

Multiple choice

A girl cycles from Lucknow to her home, a distance of 96 km, taking a rest of 6 minutes for every 6 km if her speed is 250 meters per minute. Then how much time will it take him to reach her home?

  1. 4 hour 44 min

  2. 5 hour 45 min

  3. 6 hour 30 min

  4. 7 hour 54 min
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Speed = 250 m/min = 0.25 km/min. Distance = 96 km. For every 6 km: cycling time = 6/0.25 = 24 min, plus 6 min rest = 30 min per segment. Number of segments = 96/6 = 16. Total cycling time = 16 × 24 = 384 min. Rest periods = 15 intervals × 6 = 90 min. Total time = 384 + 90 = 474 min = 7 hours 54 minutes.

Multiple choice

A man can row a distance of 720 meters against the stream in 12 minutes and returns to the starting point in 9 minutes. What is the speed (in km/h ) of the man in still water ?

  1. 4.2 km/hr

  2. 3.6 km/hr

  3. 4.8 km/hr

  4. 3.2 km/hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Speed against stream = 0.72 km / 0.2 h = 3.6 km/h. Speed with stream = 0.72 km / 0.15 h = 4.8 km/h. If v is speed in still water and u is stream speed, then v - u = 3.6 and v + u = 4.8. Solving: v = (3.6 + 4.8)/2 = 4.2 km/h.

Multiple choice

Punit goes from his home to his relative's place at a speed of 45 km/h. While returning from the relative's place, due to traffic, it takes him an hour longer as he can only drive at the speed of 40 km/h. Find the distance (in km) of his relative's place from his home?

  1. 400

  2. 720

  3. 180

  4. 360
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let distance be d km. Time going = d/45 hours. Time returning = d/40 hours. We know returning takes 1 hour longer: d/40 = d/45 + 1. Solving: Multiply by 360: 9d = 8d + 360, so d = 360 km. This is a classic time-speed-distance problem where the difference in time gives us the equation.

Multiple choice

A swimmer swims from a point P against the current for 6 min and then swims back along the current for next 6 min and reaches at a point Q. If the distance between P and Q is 120 m then the speed of the current (in km/h ) is:

  1. 0.4

  2. 0.2

  3. 1

  4. 0.6
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let swimmer's speed in still water be v m/s and current speed be s m/s. Against current for 6 min (360 sec): distance = (v - s) × 360. With current for 6 min (360 sec): distance = (v + s) × 360. Net displacement between P and Q = distance with current - distance against current = [(v + s) - (v - s)] × 360 = 2s × 360 = 720s meters. Given net displacement is 120 m, so 720s = 120, s = 120/720 = 1/6 m/s = (1/6) × (3600/1000) km/h = 0.6 km/h.

Multiple choice

The distance of the School and house of Suresh is 80 km. One day he was late by 1 hour than the normal time to leave for the college, so he increased his speed by 4 km/h and thus he reached to college at the normal time. What is the changed speed of Suresh?

  1. 28 km/h

  2. 25 km/h

  3. 20 km/h

  4. 24 km/h
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let original speed be x km/h. Distance = 80 km. Normal time = 80/x hours. New speed = (x+4) km/h. New time = 80/(x+4) hours. Since new time is 1 hour less: 80/x - 80/(x+4) = 1. Solving: 80(x+4) - 80x = x(x+4), 320 = x² + 4x, x² + 4x - 320 = 0, (x+20)(x-16) = 0, x = 16 km/h. Changed speed = 16+4 = 20 km/h.

Multiple choice

A man rows downstream to some destination and returns in 3 hours. If the speed of the boat in still water and the speed of stream are 6 km/h and 3 km/h, respectively , then the distance of the destination from the starting place is:

  1. 6.75 km

  2. 5.55 km

  3. 3.25 km

  4. 4.20 km
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Speed of boat in still water = 6 km/h, speed of stream = 3 km/h. Downstream speed = 6 + 3 = 9 km/h. Upstream speed = 6 - 3 = 3 km/h. Total time = 3 hours. Let distance = d km. Time downstream + Time upstream = d/9 + d/3 = d/9 + 3d/9 = 4d/9 = 3. Solving: 4d = 27, d = 6.75 km.

Multiple choice

A policeman sees a chain snatcher at a distance of 500 m. He starts chasing the chain snatcher running with a speed of 5 m/s, while the policeman is chasing him with a speed of 15 m/s. What is the distance covered by the chain- snatcher when he is caught by the policeman?

  1. 200m

  2. 180m

  3. 150m

  4. 250m
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Relative speed = 15 - 5 = 10 m/s. Initial gap = 500 m. Time to catch = 500 ÷ 10 = 50 seconds. In 50 seconds, chain snatcher covers 5 × 50 = 250 m. Verification: Policeman covers 15 × 50 = 750 m, gap closed = 750 - 250 = 500 m ✓. Option D is correct.

Multiple choice

A man while going to the office increases his speed to 6/5 of his actual speed and reaches 1 hour early. Find his actual speed if the distance between his home to office is 30 km.

  1. 6 km/hr

  2. 4 km/hr

  3. 5 km/hr

  4. 7 km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When speed increases to 6/5 of actual speed, time decreases to 5/6 of actual time (inverse proportion). The time saved is 1 hour, which is 1 - 5/6 = 1/6 of actual time. So actual time = 6 hours. With distance 30 km and time 6 hours, actual speed = 30/6 = 5 km/hr. At 6/5 speed (6 km/hr), time = 30/6 = 5 hours, saving 1 hour as given.

Multiple choice

From point H, at 6:30 pm, a train starts moving towards point K at the speed of 90 km/hr. Another train starts moving from point K at 7:30 p.m. towards point H at the speed of 72 km/hr. Both the train meet at 11:30 p.m. at point J. What is the ratio of the distance HJ and KJ ?
  1. $25 : 16$
  2. $5 : 16$
  3. $36 : 25$
  4. $31 : 19$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Train from H runs for 5 hours (6:30pm to 11:30pm) at 90 km/hr = 450 km. Train from K runs for 4 hours (7:30pm to 11:30pm) at 72 km/hr = 288 km. Ratio HJ:KJ = 450:288 = 25:16 after dividing by 18. Option B reverses the ratio. Options C and D don't match the calculation.

Multiple choice

Aman drove from home to a town at the speed of 60 km/hr and on his return journey, he drove at the speed of 30 km/hr and also took an hour longer to reach home. What distance did he cover each way?

  1. 75 km

  2. 55 km

  3. 60 km

  4. 80 km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance = d km. Time going = d/60 hours, time returning = d/30 hours. Since return took 1 hour longer: d/30 - d/60 = 1. Solving: (2d-d)/60 = 1, so d/60 = 1, giving d = 60 km. The key insight is that slower speed (30 km/hr vs 60 km/hr) means more time for the same distance.

Multiple choice

A boat covers a distance of 30 km. in 2 hours 30 minutes down the stream and returns back against the stream in 3 hours 45 minutes. Find the speed of the boat in still water. एक नाव धारा की दिशा में 30 किमी. दूरी 2 घंटे 30 मिनट में तय करती है तथा धारा के विपरीत इतनी दूरी तय करने में इसे 3 घंटे 45 मिनट लगते हैं | स्थिर जल में नाव की चाल ज्ञात कीजिये |

  1. 2 km/hr. 2 किमी./घंटा

  2. 6 km/hr. 6 किमी./घंटा

  3. 8 km/hr. 8 किमी./घंटा

  4. 10 km/hr. 10 किमी./घंटा

  5. 12 km/hr. 12 किमी./घंटा
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Downstream speed: 30/2.5 = 12 km/hr. Upstream speed: 30/3.75 = 8 km/hr. Still water speed = (downstream + upstream)/2 = (12 + 8)/2 = 10 km/hr. This formula works because downstream = boat + stream, upstream = boat - stream.

Multiple choice

A man travel a certain distance by train 35 km/hr and walk back 6 km/hr. The whole journey took 8hr12min. What distance did he travel by train ? एक आदमी ट्रेन से 35 किमी/घंटा की गति से एक निश्चित दूरी तय करता है और 6 किमी/घंटा की गति से वापस आता है। पूरी यात्रा में 8 घंटे 12 मिनट का समय लगा। उसने ट्रेन से कितनी दूरी तय की?

  1. 30 km 30 किमी

  2. 35 km 35 किमी

  3. 42 km 42 किमी

  4. 25 km 25 किमी

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

Let one-way distance = d km. Time by train = d/35 hr, walking back = d/6 hr. Total time = 8hr 12min = 8.2hr = 41/5 hr. So d/35 + d/6 = 41/5. Common denominator 210: 6d + 35d = 41 × 42. 41d = 1722, so d = 42 km.