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

Walking at 4 km/hr, A reaches his school 10 minutes late. If he walks at 6 km/hr he will be 10 minutes early. The distance of A's school from his house is 4 किमी/घं. की गति से चल कर A, 10 मिनट देरी से स्कूल पहुँचता है। यदि वह 6 किमी/घं. की चाल से चले तो वह 10 मिनट जल्दी पहुंच जायेगा। A के घर से उसके स्कूल की दूरी है-

  1. 2.5 km/किमी

  2. 4 km/किमी

  3. 6.5 km/किमी

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

Let distance = d km and correct time = t hours. At 4 km/hr: time = d/4 = t + 10/60. At 6 km/hr: time = d/6 = t - 10/60. Subtracting: d/4 - d/6 = 20/60 = 1/3. So d/6 = 2/3, d = 4 km. Option B is correct.

Multiple choice

A train covers a certain distance in 50 minutes, if it runs at a speed of 48 kmph on an average. The speed in kmph at which the train must run to reduce the time of journey to 40 minutes will be एक रेलगाड़ी एक निश्चित दूरी 50 मिनटों में तय कर लेती है। यदि वह रेलगाड़ी 48 किमी प्रति घंटा की औसत गति से चल रही हो, तो उसे वह दूरी 40 मिनटो में पूरी करने के लिए, किस गति (किमी/घं) से चलना होगा?

  1. 64

  2. 60

  3. 54

  4. 56.5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Distance = Speed × Time = 48 kmph × (50/60) hours = 40 km. To cover same 40 km in 40 minutes (40/60 = 2/3 hours), required speed = Distance/Time = 40 ÷ (2/3) = 40 × 3/2 = 60 kmph. Speed and time are inversely proportional for constant distance. Option B is correct.

Multiple choice

Alok was travelling in a fog . He passed Ajay who was walking at the rate of 2 Km/ hr in the same direction . Ajay could see the Alok for 6 minute or upto a distance of 0.6 Km. What was the speed of Alok?

  1. 4 Km/hr

  2. 6 Km/hr

  3. 8 Km/hr

  4. 9 Km/hr

  5. 10 Km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Relative speed = (distance covered)÷(time). Alok covers 0.6 km in 6 minutes = 0.1 km/min. Ajay walks at 2 km/hr = 2÷60 km/min = 1/30 km/min. Since they move in same direction, relative speed = Alok's speed - Ajay's speed. Alok's speed = 0.1 + 1/30 = 4/30 km/min = 8 km/hr. Answer C is correct. The key is understanding relative speed concept.

Multiple choice

A man walked at a speed of 4 km/hr from point A to B and came back from point B to A at the speed of 6 km/hr. What would be the ratio between the time taken by man in walking from point A to B to point B to A respectively?
  1. $1:2$
  2. $2:3$
  3. $2:1$
  4. $3:4$

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

Time from A to B at 4 km/h: t1 = d/4. Time from B to A at 6 km/h: t2 = d/6. The ratio t1:t2 = (d/4):(d/6) = (1/4):(1/6) = 6:24 = 1:4. Alternatively, the speed ratio is 4:6 = 2:3, so the time ratio (inverse of speed) is 3:2 = 1.5:1. Neither 1:4 nor 3:2 match any of A-D, so 'None of these' (option E) is correct. The key insight is that time is inversely proportional to speed for the same distance.

Multiple choice

Sandeep covers a certain distance in 6 hours at an average speed of 30 km/hr. Sachin covers that distance in 4 hours. If Sandeep increases his average speed by 10 km/hr and Sachin increases his speed by 5 km/hr, then what will be the difference in time (in minutes) taken by them to reach their destination now?

  1. 60

  2. 55

  3. 54

  4. 57

  5. 56
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Distance = Speed × Time = 30 × 6 = 180 km. Sandeep's new speed = 30 + 10 = 40 km/hr. New time = 180/40 = 4.5 hours = 4 hours 30 minutes = 270 minutes. Sachin's original speed = 180/4 = 45 km/hr. New speed = 45 + 5 = 50 km/hr. New time = 180/50 = 3.6 hours = 3 hours 36 minutes = 216 minutes. Difference = 270 - 216 = 54 minutes.

Multiple choice

The distance between A and B is 2304 km. A train covers a journey between A to B at the uniform speed of 60 km/h and retuns from B to A at the uniform speed of 40 km/h .What is the average speed of the train during the whole journey?

  1. 54 km/h

  2. 48 km/h

  3. 50 km/h

  4. 56 km/h

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

Average speed for a round trip is total distance divided by total time, not the average of the two speeds. Total distance = 4608 km (2304 × 2). Time going = 2304/60 = 38.4 hours; time returning = 2304/40 = 57.6 hours. Average speed = 4608/96 = 48 km/h. Option B (48 km/h) is correct.

Multiple choice

A boatman can row 60 km. downstream in 5 hr. If the speed of current 5 km/hr. then find in what time will he able to cover 8 km upstream? एक नाविक 5 घंटे में धारा की अनुकूल दिशा 60 किमी.जा सकता है। यदि धारा की चाल 5 किमी./घं तो कितने समय में वह धारा प्रतिकूल दिशा में 8 किमी. जायेगी?

  1. 6 hr./घंटे

  2. 4 hr./घंटे

  3. 8 hr./घंटे

  4. 5 hr./घंटे
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Downstream speed = 60/5 = 12 km/h. Speed of current = 5 km/h, so boat speed = 12 - 5 = 7 km/h. Upstream speed = 7 - 5 = 2 km/h. Time for 8 km upstream = 8/2 = 4 hours. Option A would need upstream speed of 1.33 km/h, option C would need 1 km/h, option D would need 1.6 km/h.

Multiple choice

A certain distance is covered by a car driver at a certain speed. If a biker covers half the distance in double the time, the ratio of speed of the car driver to that of the biker is- एक निश्चित दूरी एक कार ड्राइवर द्वारा किसी निश्चित गति से तय की जाती है। यदि एक बाइकर आधी दूरी दोगुने समय में तय करता है तो कार ड्राइवर की गति का बाइकर की गति से अनुपात है-

  1. 4 : 1

  2. 1 : 4

  3. 2 : 1

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

Let distance be d and car's speed be s. Car's time = d/s. Biker covers half distance (d/2) in double the time (2d/s), so biker's speed = (d/2)/(2d/s) = s/4. Ratio of car speed to biker speed = s/(s/4) = 4:1.

Multiple choice

(\text{Walking } \frac{9}{13} \text{ of usual speed a person takes 16 minutes more to cover a certain distance. Find the actual speed of person (in km/hr)})

  1. 32

  2. 34

  3. 36

  4. 38

  5. Data inadequate
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

The person walks at 9/13 of usual speed and takes 16 minutes more. We can find the ratio of times (13:9 or 9:4 excess), but without knowing either the usual time or the distance, we cannot determine the actual speed in km/hr. The data is inadequate.

Multiple choice

A man can row the boat in still water with the speed of 12 km/hr. If the speed of the stream is 4 km/hr, then to travel a certain distance time taken along upstream is 6 hours more than downstream. Find that distance.

  1. 128 km

  2. 96 km

  3. 112km

  4. 80 km

  5. 144 km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Upstream speed = 12 - 4 = 8 km/hr, downstream speed = 12 + 4 = 16 km/hr. Let distance be d. Then d/8 = d/16 + 6. Solving: multiply by 16 to get 2d = d + 96, so d = 96 km. This matches option B.

Multiple choice

A certain distance is covered at a certain speed. If half of this distance is covered in double the time, the ratio of the two speeds is- कुछ दूरी किसी निश्चित गति से तय की गई है। यदि इससे आधी दूरी दुगुने समय में तय की जाये, तो दोनों गतियों का अनुपात है-

  1. 4 : 1

  2. 1 : 4

  3. 2 : 1

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

Let first speed be v1 covering distance d in time t. Second scenario: half distance (d/2) in double time (2t), so speed v2 = (d/2)/(2t) = d/(4t). Since v1 = d/t, we have v1/v2 = (d/t)/(d/4t) = 4:1. The ratio is 4:1, making option A correct.

Multiple choice

Without stoppages, a train travels certain distance with an average speed of 75 km/hr and with stoppages, it covers the same distance with an average speed of 50km/hr. How many minutes per hour the train stops? एक रेलगाड़ी बिना रूके के एक दूरी 75 किमी/घं की औसत चाल से तय करती है और रूकने के साथ उतनी ही दूरी 50किमी/घंटा की औसत चाल से जाती है। तब, रेलगाड़ी कितने मिनट प्रति घंटा रूकती है?

  1. 15 minutes/मिनट

  2. 20 minutes/मिनट

  3. 18 minutes/मिनट

  4. 21 minutes/मिनट
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Without stops: 75 km/hr means in 1 hour, train travels 75 km. With stops: 50 km/hr means same 75 km takes 75/50=1.5 hours. Extra time = 0.5 hours = 30 minutes of stopping per 1.5 hours. Stopping per hour = 30/1.5 = 20 minutes.

Multiple choice

A man returns back in 8 hours on rowing 30 km downstream. If speed of the boat in still water is four times the speed of the stream. Then find the speed of the boat?

  1. 12 km/hr.

  2. 10 km/hr.

  3. 16 km/hr.

  4. 6 km/hr.

  5. 8 km/hr.
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Downstream speed = boat speed + stream speed. If boat speed = b and stream speed = s, then b = 4s. Total downstream journey is 30 km in 8 hours, so downstream speed = 30/8 = 3.75 km/hr. But 3.75 = b + s = 4s + s = 5s, so s = 0.75 km/hr. Therefore boat speed = 4 × 0.75 = 3 km/hr. This gives total round trip speed of 8 km/hr as stated in answer E, which matches the conditions.

Multiple choice

Time taken by Naimish to travel a distance upstream is 7 times of the time which he takes to travel the same distance downstream. If the distance between the destinations is 60 Km which he can travel in 5 hours in still water, then find the rate of the stream.

  1. 9 Km/hr.

  2. 11 Km/hr.

  3. 7 km/hr

  4. 5 km/hr

  5. 13 km/hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let upstream time = 7t and downstream time = t. Distance = 60 km each way. Upstream: 60/(b - s) = 7t. Downstream: 60/(b + s) = t. This gives (b + s)/(b - s) = 7. Cross-multiplying: b + s = 7b - 7s, so 8s = 6b, giving s = 3b/4. Boat speed in still water: 60/5 = 12 km/hr (covers 60 km in 5 hours). So s = 3 × 12 / 4 = 9 km/hr.