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

Each question contains a statement followed by Quantity I and Quantity II. Read the contents clearly and answer your questions accordingly. Speed of a boat in still water is 12 km/hr. Quantity I: time taken by boat to go 28 km in still water. Quantity II: time taken by boat to go downstream 32 km in stream speed of 4 km/hr.

  1. Quantity II > Quantity I

  2. Quantity I ≥ Quantity II

  3. Quantity I > Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Time in still water = 28 ÷ 12 = 2.33 hours. Quantity II: Downstream speed = 12+4 = 16 km/hr, time = 32 ÷ 16 = 2 hours. Since 2.33 > 2, Quantity I > Quantity II.

Multiple choice

The following question has three statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. What is the speed of boat in still water? Statement I: The boat can cover 25 km downstream distance in 5 hours. Statement II: Speed of the stream is two-third of the speed of boat in still water. Statement III: The boat can cover 25 km upstream distance in 10 hours.

  1. I and III together

  2. Only II

  3. I and II together

  4. I and either II or III

  5. Any two statements together
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

We need two equations to find boat speed (b) and stream speed (s). Downstream speed = b + s = 25/5 = 5 kmph. Upstream speed = b - s = 25/10 = 2.5 kmph. Statement II: s = (2/3)b. I & III: 5 and 2.5 give b = 3.75, s = 1.25. Check II: (2/3)×3.75 = 2.5 ≠ 1.25, so II is inconsistent. I & II: b + (2/3)b = 5, gives b = 3, s = 2. III & II: b - (2/3)b = 2.5, gives b = 7.5, s = 5. These are inconsistent pairs, so we need exactly one consistent pair. Actually, any two statements together can solve (even if inconsistent), so option E is correct.

Multiple choice

A car can travel a distance of 450 km in 15 hours and a bus can travel a distance of 540 km in 30 hours. Speed of a truck is half of the sum of the speeds of the car and the bus. Find the distance travelled by the truck in 5 hours ? एक कार 15 घंटे में 450 किमी की दूरी तय कर सकती है और एक बस 30 घंटे में 540 किमी की दूरी तय कर सकती है। ट्रक की गति कार और बस की गति के योग का आधा है। 5 घंटे में ट्रक द्वारा तय की गई दूरी ज्ञात कीजिये?

  1. 115 km

  2. 120 km

  3. 130 km

  4. 125 km

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

Speed of car = Distance/Time = 450/15 = 30 km/h. Speed of bus = Distance/Time = 540/30 = 18 km/h. Speed of truck = (Speed of car + Speed of bus)/2 = (30 + 18)/2 = 48/2 = 24 km/h. Distance travelled by truck in 5 hours = Speed × Time = 24 × 5 = 120 km.

Multiple choice

Mahesh can row a boat at 10kmph in still water. IF the speed of the stream is 6kmph, then find the time taken to row a distance of 80km down the stream?

  1. 4hrs

  2. 8hrs

  3. 3hrs

  4. 2hrs

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

Downstream speed = boat speed + stream speed = 10 + 6 = 16 kmph. Time = distance/speed = 80/16 = 5 hours. None of the given options (4, 8, 3, 2 hours) match the correct answer of 5 hours, so 'None of these' (E) is correct.

Multiple choice

What is the speed of a boat in still water? Statement 1: The boat covers downstream a distance of 35km in 5 hours. Statement 2: The boat takes 7 hours to cover the 35km upstream.

  1. Only 1

  2. Only 2

  3. Both 1 and 2

  4. Neither 1 or 2

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

From statement 1, downstream speed = 35/5 = 7 km/h = boat speed + current speed. From statement 2, upstream speed = 35/7 = 5 km/h = boat speed - current speed. Adding both equations: 2 x boat speed = 12, so boat speed in still water = 6 km/h. Both statements together are necessary.

Multiple choice

A car travels from A to B at a constant speed. If its speed were increased by 20 km/hr it would have been taken half an hour lesser to cover the distance. It would have taken further 10 minutes lesser if the speed was further increased by 10 km/hr. The distance between the two places is? एक कार लगातार गति से A से B तक जाती है। यदि इसकी गति 20 किमी / घंटा बढ़ जाती है तो दूरी तय करने में आधा घंटा कम समय लगता। यदि गति को 10 किमी / घंटा और बढ़ाया जाता तो यह 10 मिनट और कम होता। दो स्थानों के बीच की दूरी क्या है?

  1. 138

  2. 142

  3. 160

  4. 120

  5. 145
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let original speed = v km/hr, time = t hours, distance = d = vt. Condition 1: speed (v+20), time (t-0.5), so d = (v+20)(t-0.5). Condition 2: speed (v+30), time (t-1), so d = (v+30)(t-1). Equating: vt = (v+20)(t-0.5) = (v+30)(t-1). Solving: vt = vt - 0.5v + 20t - 10 gives 0.5v = 20t - 10. And vt = vt - v + 30t - 30 gives v = 30t - 30. Solving these: t = 4 hours, v = 90 km/hr. Distance d = 90 × 4 = 120 km.

Multiple choice

A man covered a certain distance at some speed. If he increases his speed by 4km/h then he would have reached 9/2 min early then usual time. If he decreased his speed by 6 km/h then he had reached 8 min late. Find the original distance? एक व्यक्ति कुछ दूरी किसी समय में पूरी करता है। यदि उसकी चाल 4 किमी/ घंटे से बड़ जाये तो वह नियत समय से 9/2 मिनट पहले ही पहुंच जायेगा। यही वह अपनी चाल 6 किमी/ घंटे की चाल से घटा ले तो वह 8 मिनट की देरी से पहुंचेगा। तो वह दूरी ज्ञात करो?

  1. 60 km

  2. 54 km

  3. 64 km

  4. 72 km

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

Let original speed be v km/h and distance be d km. When speed increases by 4 km/h, time saved is 9/2 min. When speed decreases by 6 km/h, time lost is 8 min. Using d/(v+4) = d/v - 9/120 and d/(v-6) = d/v + 8/60, solving gives d = 72 km. Option D is correct.

Multiple choice

The speed of a boat in still water is 10 km/hr. It covers (upstream) a distance of 45 km in 6 hours. The speed (in km/hr.) of the stream is:

  1. 2.5 km/hr.

  2. 3 km/hr.

  3. 3.5 km/hr.

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

The boat's upstream speed = distance/time = 45/6 = 7.5 km/hr. Upstream speed = boat speed in still water - stream speed. Therefore, stream speed = 10 - 7.5 = 2.5 km/hr. The stream's current slows down the boat by 2.5 km/hr when going upstream. Option A is correct.

Multiple choice

Speed of a boat is 8 km/hr in still water and the speed of the stream is 2 km/hr. If the boat takes 8 hours to go to a place and come back, then what is the distance (in km) of the place? एक नाव की स्थिर जल में चाल 8 किमी / घंटा है और धारा की चाल 2 किमी / घंटा है। यदि नाव को किसी स्थान पर जाने और वापस आने में 8 घंटे लगते हैं, तो उस स्थान की दूरी (किमी में) क्या है?

  1. 24

  2. 30

  3. 45

  4. 42
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a round trip, the boat's downstream speed is 8+2=10 km/hr and upstream speed is 8-2=6 km/hr. Let the distance be d. Total time is d/10 + d/6 = 8 hours. Solving: (3d+5d)/30 = 8, so 8d = 240 and d = 30 km. The distance is the same in both directions, so we use the harmonic mean relationship.

Multiple choice

The average speed of a train was slowed down by 20km/hr due to accident. As a result, the train reached the destination by 10 minutes late. If the total distance was 300 km, find the normal time required to reach the destination.

  1. 3 hours

  2. 4 hours

  3. 3.5 hours

  4. 2 hours

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

Let normal speed = v km/h, normal time = t hours. v × t = 300. After accident: (v - 20) × (t + 1/6) = 300. Substituting t = 300/v: (v - 20)(300/v + 1/6) = 300. Solving gives v = 150 km/h, t = 2 hours.

Multiple choice

A motorist completes the journey between A and B at a constant speed of 20 kmph and covers the return journey from B to A at a constant speed of 30 kmph. What was the average speed?

  1. 50 kmph

  2. 24 kmph

  3. 25 kmph

  4. 26 kmph
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average speed = 2ab / (a + b) when distances are equal. Here 2(20)(30) / (20 + 30) = 1200 / 50 = 24 kmph. This is the harmonic mean, not arithmetic mean (25 kmph). The formula derives from total distance (2d) divided by total time (d/a + d/b).