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

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. निम्नलिखित प्रत्येक प्रश्न में दिए गए कथन को पढ़िए और उसके आधार पर मात्रा I और मात्रा II की तुलना कीजिए। Quantity I : A car covers first 30 km in 30 minutes and the remaining 74 km in 50 minutes. What is the average speed of the car (in km/hr) Quantity II : 72 km/hr मात्रा I : एक कार पहले 30 किमी को 30 मिनट में और शेष 74 किमी को 50 मिनट में तय करती है। कार की औसत गति क्या है (किमी/घंटा में) मात्रा II: 72 किमी/घंटा

  1. Quantity : I > Quantity : II मात्रा : I > मात्रा : II

  2. Quantity : I ≥ Quantity : II मात्रा : I ≥ मात्रा : II

  3. Quantity : I < Quantity : II मात्रा : I < मात्रा : II

  4. Quantity : II ≥ Quantity : I मात्रा : II ≥ मात्रा : I

  5. Quantity I = Quantity II or relation can't be established मात्रा I = मात्रा II या संबंध स्थापित नहीं किया जा सकता
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Total distance = 30 + 74 = 104 km. Total time = 30 + 50 = 80 minutes = 80/60 hours = 4/3 hours. Average speed = 104/(4/3) = 78 km/hr. Quantity II = 72 km/hr. Since 78 > 72, Quantity I > Quantity II.

Multiple choice

A person travels for 3 hours at the speed of 40 km/h and 4.5 hrs the speed of 60 km/h. at the end of it, he finds that he has covered 3/5 of the total distance at what average speed should he travel to cover the remaining distance in 4 hrs एक व्यक्ति 3 घंटे 40 किमी/घंटा की गति से और 4.5 घंटे 60 किमी/घंटा की गति से यात्रा करता है। इसके अंत में, वह पाता है कि उसने कुल दूरी का 3/5 भाग तय किया है, शेष दूरी को 4 घंटे में तय करने के लिए उसे कितनी औसत गति से यात्रा करनी चाहिए?

  1. 55 km/hr 55 किमी/घंटा

  2. 65 km/hr 65 किमी/घंटा

  3. 40 km/hr 40 किमी/घंटा

  4. 45 km/hr 45 किमी/घंटा

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

Distance covered in first part: 3 hours × 40 km/h = 120 km. Distance covered in second part: 4.5 hours × 60 km/h = 270 km. Total covered = 390 km. This is 3/5 of total distance, so total distance = 390 × 5/3 = 650 km. Remaining distance = 650 - 390 = 260 km. To cover 260 km in 4 hours: speed = 260/4 = 65 km/h.

Multiple choice

A train covers certain distance in two parts. Distance covered in first part is 200% more than the distance covered in second part while speed of train is in the ratio 2 : 1in first and second part respectively. If average speed of train is 64 km/hr, then find the speed of train in first part? (In kmph) एक ट्रेन निश्चित दूरी को दो भागों में तय करती है। पहले भाग में तय की गई दूरी दूसरे भाग में तय की गई दूरी से 200% अधिक है जबकि ट्रेन की गति पहले और दूसरे भाग में क्रमशः 2: 1 के अनुपात में है। यदि ट्रेन की औसत गति 64 किमी/घंटा है, तो पहले भाग में ट्रेन की गति ज्ञात कीजिए? (किमी प्रति घंटे में)

  1. 80

  2. 45

  3. 40

  4. 90

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

Let distance in second part be d. Then distance in first part = d + 200% of d = 3d. Let speed in second part be v. Then speed in first part = 2v. Time in first part = 3d/2v = 1.5d/v. Time in second part = d/v. Total distance = 4d, total time = 2.5d/v. Average speed = 4d ÷ 2.5d/v = 1.6v = 64 km/h, so v = 40 km/h and 2v = 80 km/h.

Multiple choice

A person covers a distance of 300 km and then returns to the starting point. The time taken by him for the outward journey is 5 hours more than the time taken for the return journey. If he returns at a speed of 10km/h more than the speed of going, What was the speed (in km/h) for the outward journey? एक व्यक्ति 300 किमी की दूरी तय करता है और फिर प्रारंभिक बिंदु पर लौट आता है। उसके द्वारा बाहरी यात्रा के लिए लिया गया समय वापसी यात्रा के लिए लिए गए समय से 5 घंटे अधिक है। यदि वह जाने की गति से 10 किमी/घंटा अधिक की गति से लौटता है, तो बाहरी यात्रा के लिए गति (किमी/घंटा में) क्या थी?

  1. 20

  2. 15

  3. 25

  4. 30

  5. 29
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let outward speed = v km/h. Return speed = v + 10 km/h. Time outward = 300/v hours, time return = 300/(v+10) hours. Given: 300/v = 300/(v+10) + 5. Solving: 300(v+10) = 300v + 5v(v+10), giving v² + 10v - 600 = 0. Using quadratic formula: v = (-10 + √2500)/2 = 20 km/h (rejecting negative solution).

Multiple choice

The distance between the places H and O is D units. The average speed that gets a person from H to O in a stipulated time is S units. He takes 20 minutes more time than usual if he travels at 60 km/h, and reaches 44 minutes early if he travels 75 km/h. The sum of the numerical values of D and S is: H और O स्थानों के बीच की दूरी D इकाई है। एक निर्धारित समय में किसी व्यक्ति को H से O तक प्राप्त करने वाली औसत गति S इकाई है। यदि वह 60 किमी/घंटा की गति से यात्रा करता है तो वह सामान्य से 20 मिनट अधिक समय लेता है, और यदि वह 75 किमी/घंटा की यात्रा करता है तो 44 मिनट पहले पहुंच जाता है। D और S के संख्यात्मक मानों का योग है:

  1. 358

  2. 384

  3. 376

  4. 344

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

Let usual time be T hours. At 60 km/h: D/60 = T + 20/60 = T + 1/3. At 75 km/h: D/75 = T - 44/60 = T - 11/15. Subtracting: D/60 - D/75 = 1/3 + 11/15 = 16/15. So D(1/60 - 1/75) = 16/15, giving D × 1/300 = 16/15, so D = 320 km. Then S = 320/(T + 1/3). From D/60 = T + 1/3: 320/60 = 16/3, so T = 5 hours. S = 320/5 = 64 km/h. D + S = 320 + 64 = 384. Option A (358) and C (376) don't satisfy both conditions.

Multiple choice

Two cities A and B are at a distance of 240 km from each other. Two persons P and Q start from First city at a speed of 20 km/hr and 10 km/hr respectively. P reached the second city B and returns back and meets Q at Y. Find the distance between A and Y. दो शहर A और B एक दूसरे से 240 किमी की दूरी पर हैं। दो व्यक्ति P और Q पहले शहर से क्रमशः 20 किमी/घंटा और 10 किमी/घंटा की गति से चलना शुरू करते हैं। P दूसरे शहर B तक पहुँचता है और वापस लौटता है और Y पर Q से मिलता है। A और Y के बीच की दूरी ज्ञात कीजिए।

  1. 40 km 40 किमी

  2. 80 km 80 किमी

  3. 70 km 70 किमी

  4. 60 km 60 किमी

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

P takes 240/20=12 hours to reach B. In 12 hours, Q travels 12×10=120km from A. When P returns, they meet at Y. Since P and Q travel toward each other after P reaches B, their meeting point is determined by their speeds. The distance from A to Y is 80km. Option A (40km) would mean they meet much earlier. Option C (70km) and D (60km) don't account for the full travel time correctly.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question ? How much distance did the train cover ? I. The average speed of train is 40 km/hr. II. During its 8 hours journey it runs 3 hours at 75 km./hr. and 5 hours at 45 km/hr.

  1. statement I alone is sufficient but statement II alone is not sufficient.

  2. statement II alone is sufficient but statement I alone is not sufficient.

  3. each statement alone (either I or II) is sufficient.

  4. statement I and II together are not sufficient.

  5. both statement together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement II alone is sufficient. Distance = speed × time. Given: 3 hours at 75 km/hr + 5 hours at 45 km/hr. Distance = (3 × 75) + (5 × 45) = 225 + 225 = 450 km. Statement I only gives average speed (40 km/hr) without time or distance, which is insufficient alone.

Multiple choice

A train meet with an accident 120 km. station A. It completed the remaining journey at 4/5 of its previous speed and reached 2 hour late at station B. Had the accident taken place 200 km further, it would have been only 1 hour late. What is the speed of the trian ? एक ट्रेन स्टेशन A से 120 किमी. दूर दुर्घटनाग्रस्त हो जाती है। यह शेष दूरी को अपनी प्रारम्भिक चाल के 4/5 भाग A चाल से तय करती है और 2 घंटे विलम्ब से पहुँचती है स्टेशन B पर। यदि दुर्घटना 200 किमी. और बाद में होती तो 1 घंटा विलम्ब होता। ट्रेन की चाल ज्ञात कीजिए।

  1. 60 km/hr./किमी/घंटा

  2. 50 km/hr./किमी/घंटा

  3. 80 km/hr./किमी/घंटा

  4. 75 km/hr./किमी/घंटा
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let original speed be v. At 4/5 speed, time becomes 5/4 of original, so extra time is distance/20v. From the two scenarios, the 200 km segment causes 1 hour difference, giving v = 50 km/hr. The delay decreases by half when accident point moves 200 km further.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question ? What is the speed of a car? (I) The car covers a distance of 270 km in 5 hrs. (II) The car covers a distance of 540 km in 10 hrs.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statements together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I gives speed = distance/time = 270/5 = 54 km/hr. Statement II gives speed = 540/10 = 54 km/hr. Since each statement independently provides sufficient data to calculate speed, option C is correct.

Multiple choice

A person walks along a straight road from his house to a market $2.5\ km$ away with a speed of $5\ km/hr$ and instantly turns back and reaches the house with a speed of $7.5\ km/hr$. The average speed of the person during the time interval $0$ to $50$ $minutes$ is (in $m/s$):
  1. $\displaystyle 4\frac{2}{3}$
  2. $\displaystyle\frac{5}{3}$
  3. $\displaystyle\frac{5}{6}$
  4. $\displaystyle\frac{1}{3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total distance = 2.5 km out + 2.5 km back = 5 km. Time out = 2.5/5 = 0.5 hr = 30 min. Time back = 2.5/7.5 = 1/3 hr = 20 min. Total time = 50 min. Average speed = Total distance / Total time = 5 km / (50/60) hr = 6 km/hr. 6 km/hr = 6 * (1000/3600) m/s = 60/36 = 5/3 m/s.

Multiple choice

A man wants to reach a certain destination. One-sixth of the total distance is muddy while half the distance is tar road. For the remaining distance he takes a boat. His speed of travelling in mud, in water, on tar road is in the ration $3 : 4 : 5$. The ratio of the duration he requires to cross the patch of mud, stream and tar road is
  1. $\dfrac { 1 }{ 2 } : \dfrac { 4 }{ 3 } : \dfrac { 5 }{ 2 } $
  2. $3 : 8 : 15$
  3. $10 : 15 : 18$
  4. $1 : 2 : 3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a total distance D, the mud, water, and tar distances are D/6, D/3, and D/2. Dividing each distance by its speed ratio 3:4:5 gives times proportional to D/18, D/12, and D/10, which simplify to 10:15:18.

Multiple choice

A body covers one third of the distance with speed ${V_1}$ and two third of the distance with speed ${V_2}$. The average speed of the body is:
  1. $\frac{{{V_1} + {V_2}}}{2v_2}$
  2. $\frac{{{V_1} + {V_2}}}{2}$
  3. $\frac{{3{V_1}{V_2}}}{{2{V_1} + {V_2}}}$
  4. $\frac{{3{V_1}{V_2}}}{{{V_1} + 2{V_2}}}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average speed = Total distance / Total time. Let total distance be D. Time = (D/3)/V1 + (2D/3)/V2 = D(V2 + 2V1) / (3V1V2). Average speed = D / (D(V2 + 2V1) / 3V1V2) = 3V1V2 / (2V1 + V2).

Multiple choice

A bird is tossing (flying to and fro) between two cars moving towards each other on a straight road. One car has speed of 27 km $h^{-1}$ while the other has the speed of 18 km $h^{-1}$. The bird starts moving from first car towards the other and is moving with the speed of 36 km $h^{-1}$ when the two were separated by 36 km. The total distance covered by the bird is

  1. 28.8 km

  2. 38.8 km

  3. 48.8 km

  4. 58.8 km
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Relative speed of cars = 27 + 18 = 45 km/h. Time to meet = 36 km / 45 km/h = 0.8 hours. The bird flies at 36 km/h for the entire duration. Distance = 36 * 0.8 = 28.8 km.