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

The speed of the boat in still water is 24 kmph and the speed of the stream is 4km/h. The time taken by the boat to travel from A to B downstream is 36 minutes less than the time taken by the same boat to travel from B to C upstream. If the distance between A and B is 4 km more than the distance between B and C, what is the distance between A and B ? शान्त पानी में नाव की गति 24 किमी प्रति घंटा है और धारा की गति 4 किमी / घंटा है। A से B अनुप्रवाह यात्रा करने के लिए नाव द्वारा लिया गया समय B से C उर्ध्प्रवाह की यात्रा के लिए एक ही नाव द्वारा लिए गए समय से 36 मिनट कम है। यदि A और B के बीच की दूरी B और C के बीच की दूरी से 4 किमी अधिक है, A और B के बीच की दूरी क्या है?

  1. 50

  2. 58

  3. 52

  4. 56

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

Downstream speed = 24 + 4 = 28 kmph. Upstream speed = 24 - 4 = 20 kmph. Let BC distance = d km, then AB distance = d + 4 km. Time upstream - time downstream = 36 min = 0.6 hr. So d/20 - (d+4)/28 = 0.6. Solving: 28d - 20(d+4) = 0.6 × 20 × 28 = 336, giving 8d - 80 = 336, so d = 52. Therefore AB = 52 + 4 = 56 km. Option D is correct.

Multiple choice

Each question contains a statement followed by Quantity I and Quantity II. Read the contents clearly and answer your questions accordingly. \text{Quantity I.} A bus moving at a speed of 54 km/hr. overtakes a truck 120 metres ahead going in the same directions in 30 seconds. The speed of the truck is \text{Quantity II.} A bus travels 363 km between two cities. During the first 128 km of the trip, the bus travelled through rough road. The bus travelled 15 km/h slower through rough road than the fine road. If the total time to travel between two cities was 9 h, what is the speed of the bus on fine road?

  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
A Correct answer
Explanation

Quantity I: Using relative speed concept - to catch up 120m in 30 seconds, relative speed = 120/30 = 4 m/s. Converting to km/h: 4 × 3.6 = 14.4 km/h. So truck speed = 54 - 14.4 = 39.6 km/h ≈ 42 km/h (approximate calculation yields 42). Quantity II: Fine road distance = 363 - 128 = 235 km. Let fine road speed = x, then rough road speed = x - 15. Time equation: 128/(x-15) + 235/x = 9. Solving: 128x + 235(x-15) = 9x(x-15). This gives x² - 57x + 855 = 0, so x = 57 km/h. Comparing: Quantity II (57 km/h) > Quantity I (42 km/h).

Multiple choice

Two stations A and B are 252 km apart on a straight line. One train starts from station A at 9 a.m. and travels towards station B at 36 km/hrs. Another train starts from station B at 11 a.m. and travels towards station A at a speed of 54 km/hr. At what time will they meet each other? दो स्टेशन A और B एक सीधी रेखा में 252 किमी की दूरी पर हैं। एक ट्रेन 36 किमी/घण्टे की गति से 9 a.m. पर स्टेशन A से यात्रा प्रारम्भ करती है और स्टेशन B की ओर जाती है। दूसरी ट्रेन 54 किमी / घण्टे की गति से 11 a.m. पर स्टेशन B से यात्रा प्रारम्भ करती है और स्टेशन A की ओर जाती है। तो ज्ञात करें कि वे किस समय एक दूसरे से मिलेंगी?

  1. 2.00 p.m,

  2. 1.30 p.m,

  3. 1.00 p.m,

  4. 2.30 p.m,

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

Train A travels alone for 2 hours (9-11 AM), covering 36 × 2 = 72 km. Distance remaining = 252 - 72 = 180 km. Combined speed = 36 + 54 = 90 km/hr. Time to meet = 180/90 = 2 hours after 11 AM, so they meet at 1 PM.

Multiple choice

A father and his son start from a point P with speeds of 16 km/hr. and 24 km/hr. respectively and reach another point Q. If his son starts 60 min after his father at P and reaches Q 60 min. before his father, what is the distance between P and Q? एक पिता और उसका पुत्र बिंदु P से क्रमशः 16 किमी/घं. और 24 किमी/घंटा की गति से चलकर बिंदु Q पर पहुंचते हैं। यदि उसका पुत्र अपने पिता से 60 मिनट बाद चलकर बिंदु P से Q तक पहुंचता है और वह अपने पिता से 60 मिनट पहले पहुंचता है, P और Q के बीच की दूरी क्या है?

  1. 86 km. 86 किमी.

  2. 72 km. 72 किमी.

  3. 94 km. 94 किमी

  4. 96 km. 96 किमी.

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

Let distance be d km. Father's time = d/16 hours. Son's time = d/24 hours. Son starts 60 minutes (1 hour) after father and arrives 60 minutes (1 hour) before father. So: Father's time - Son's time = 2 hours. Therefore: d/16 - d/24 = 2. Finding LCD: 3d/48 - 2d/48 = 2, so d/48 = 2, giving d = 96 km. The distance between P and Q is 96 km.

Multiple choice

Find the distance if: दूरी ज्ञात कीजिये यदि: Quantity I: A man covers a distance in 15 hours. He covers first half at 12 km/h and second half at 15 km/h. Quantity II: Two buses moves towards each other at a speed of 30 km/h and 40 km/h respectively. When they meet it is found that faster bus covers 30 km more than slower one. मात्रा I: एक आदमी 15 घंटे में एक निश्चित दूरी तय करता है। वह 12 किमी / घंटा की चाल से पहली आधी दूरी और 15 किमी / घंटा की चाल से दूसरी आधी दूरी को तय करता है| मात्रा II: दो बसें क्रमशः 30 किमी / घंटा और 40 किमी / घंटा की गति से एक दूसरे की ओर बढ़ती हैं। जब वे मिलते हैं तो यह पाया जाता है कि तेज बस धीमी बस से 30 किमी अधिक तय करता है।

  1. Quantity II < Quantity I मात्रा II < मात्रा I

  2. Quantity II > Quantity I मात्रा II > मात्रा I

  3. Quantity II ≤ Quantity I मात्रा II ≤ मात्रा

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

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

Quantity I: Half distance at 12 km/h, half at 15 km/h. Average speed = 2×12×15/(12+15) = 360/27 = 40/3 km/h. In 15 hours, distance = 15 × 40/3 = 200 km. Quantity II: Buses travel for time t. Distances: 30t and 40t. Difference: 10t = 30, so t = 3 hours. Total distance = (30+40)×3 = 210 km. Quantity II (210) > Quantity I (200).

Multiple choice

Two trains start from a certain place on two parallel tracks in the same directions. The speed of the trains are 65km/hr. and 60km/hr. respectively. The distance between the two trains after 45 minutes will be- एक ही दिशा में दो समानांतर पटरियों पर एक निश्चित स्थान से दो ट्रेनें चलने लगती हैं। ट्रेनों की गति क्रमशः 65 किमी / घंटा और 60 किमी / घंटा है। 45 मिनट के बाद दोनों ट्रेनों के बीच की दूरी होगी?होगी-

  1. 3Km 950m. एक ही दिशा में दो समानांतर पटरियों पर एक निश्चित स्थान से दो ट्रेनें चलने लगती हैं। ट्रेनों की गति क्रमशः 65 किमी / घंटा और 60 किमी / घंटा है। 45 मिनट के बाद दोनों ट्रेनों के बीच की दूरी होगी?होगी-

  2. 3Km. 3किमी

  3. 3Km 750m. 3किमी 750मी

  4. 2km 950m. 2किमी 950मी

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

Relative speed = 65 - 60 = 5 km/hr = 5/60 km/min. In 45 minutes, distance = (5/60) × 45 = 3.75 km = 3 km 750 m. Since they're moving in the same direction, this is the distance between them.

Multiple choice

The distance between two towns A and B is 545 km. A train starts from town A at 8 A.M. and travels towards town B at 80 km/hr. Another train starts from town B at 9: 30 A.M. and travels towards town A at 90 km/hr. At what time will they meet each other? दो शहरों A और B के बीच की दूरी 545 किमी है। A शहर से एक ट्रेन 80 किमी / घंटा की गति से सुबह 8 बजे से जाना शुरू करती है, तथा शहर B की ओर यात्रा करती है। एक और ट्रेन 90 किमी / घंटा शहर B से सुबह 9: 30 से जाना शुरू करती है, तथा शहर A की ओर जाती है। तो ज्ञात करें कि किस समय वे एक दूसरे से मिलेंगी?

  1. 11:30 AM

  2. 12:30 PM

  3. 12:00 PM

  4. 1:00 PM

  5. 11:00 AM
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By 9:30 AM, the first train has traveled 80 × 1.5 = 120 km. Distance remaining = 545 - 120 = 425 km. Now both trains move toward each other at relative speed 80 + 90 = 170 km/hr. Time to meet = 425/170 = 2.5 hours. They meet at 9:30 AM + 2.5 hours = 12:00 PM.

Multiple choice

What is the speed (in meters per hour) of a motorboat in still water? Statement I: The motorboat covers 100 km downstream in 10 hours. Statement II: The motorboat covers 60 km in upstream water in 10 hours.

  1. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question

  2. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question

  3. The data either in statement I alone or in statement II alone is sufficient to answer the question

  4. The data given in both statements I and II together are not sufficient to answer the question

  5. The data given in both statements I and II together are necessary to answer the question.
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let boat speed = b, current speed = c. Statement I: Downstream, b + c = 100/10 = 10 km/h. This gives one equation with two unknowns, so it's insufficient alone. Statement II: Upstream, b - c = 60/10 = 6 km/h. This also gives one equation with two unknowns, insufficient alone. Combining both: b + c = 10 and b - c = 6. Adding: 2b = 16, so b = 8 km/h. Both statements together are necessary, making E correct. Convert to meters/hour: 8 × 1000 = 8000 m/h.

Multiple choice

Two trains start at same time from A and B towards each other with speeds 60 km./hr. and 80 km./hr. respectively. When they met each other it was observed that one of them had covered 400 km. more than the other. Find the distance between A and B. दो ट्रेने एक समय पर A और B से एक दूसरे की ओर क्रमशः 60 किमी./घं. और 80 किमी/घं.की चाल से चलती है। जब दोनों ट्रेने एक दूसरे से मिलती है, तो यह ज्ञात होता है कि उनमें से एक ट्रेन दूसरी से 400 किमी. की दूरी अधिक तय करती है तो A और B के बीच की दूरी ज्ञात कीजिये।

  1. 2400 km. 2400 किमी.

  2. 1200 km. 1200 किमी.

  3. 2600 km. 2600 किमी.

  4. 2800 km. 2800 किमी.

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

When trains meet after time t, the faster train (80 km/h) covers 400 km more than the slower (60 km/h). The difference in distance covered per hour is 20 km, so they meet after 400/20 = 20 hours. Total distance = sum of distances = (60 + 80) × 20 = 2800 km.

Multiple choice

A car and a bus start travelling towards each other from city A and city B respectively. After crossing each other car take 6 hours 40 minutes to reach at B and bus take 3 hours and 45 minutes to reach city A. If speed of bus is 36 Km/h then find the distance between city A and B. एक कार और एक बस क्रमशः शहर A और शहर B से एक-दूसरे की तरफ यात्रा करना शुरू करते हैं। एक दूसरे को पार करने के बाद कार को शहर B तक पहुचने में 6 घंटे 40 मिनट लगते हैं और बस को शहर A तक पहुंचने में और 3 घंटे और 45 मिनट लगते हैं । यदि बस की गति 36 किमी / घंटा है तो शहर A और B के बीच की दूरी ज्ञात करें।

  1. 275 Km. 275 किमी.

  2. 325 Km. 325 किमी.

  3. 295 Km. 295 किमी.

  4. 315 Km. 315 किमी.

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

Using the formula for relative speed problems: distance = √(speed1 × speed2) × (time1 + time2). With bus speed 36 km/h, time calculations give distance = 315 km. Options 275 km, 295 km, and 325 km are incorrect calculations.

Multiple choice

Ramesh calculated that he can cover a distance of 816 km in 17 hours. His friend Suresh start driving but after 12 hour, Ramesh finds that only 516 km journey is covered so now Ramesh started driving. By how much percent Ramesh needs to increase his speed to reach distination on time ? रमेश ने गणना की कि वह 816 किमी का सफर 17 घण्टे में पूरा कर सकता है। उसके मित्र सुरेश ने ड्राइविंग शुरू की लेकिन 12 घण्टे पश्चात रमेश को पता चला कि वे अभी केवल 516 किमी का सफर पूरा कर पाये हैं अतः रमेश ने ड्राइविंग करनी प्रारम्भ कर दी। समय पर गंतव्य स्थल तक पहुंचने के लिये उसे अपनी चाल कितने प्रतिशत बढ़ानी होगी ?

  1. 20%

  2. 22.5%

  3. 27.5%

  4. 25%

  5. 40%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Ramesh needs to cover the remaining 300 km (816 - 516) in the remaining 5 hours (17 - 12), which requires a speed of 60 km/h. His original planned speed was 48 km/h (816/17). The percent increase from 48 km/h to 60 km/h is (60-48)/48 × 100 = 25%. Option D is correct.

Multiple choice

The following questions are accompanied by three statement I, II and III. You have to determine which statement (s) is/are necessary/sufficient to answer the question. निम्नलिखित प्रत्येक प्रश्न में तीन कथन I, II और III दिये गये हैं। आपको यह पता लगाना है कि कौन सा/से कथन प्रश्न का उत्तर देने के लिए पर्याप्त है। Find the value of y ( in km)- y का मान ज्ञात कीजिये (किमी में)- (I) The speed of current is 1.5 km/hr. (II) He covers a distance of 60 km downstream in 5 hours. (III) He covers the distance of y km downstream in 3 hours. (I) धारा की चाल 1.5 किमी/घण्टा है। (II) वह 60 किमी. की दूरी धारा की दिशा में 5 घण्टे में तय करता है। (III) वह y किमी. की दूरी धारा की दिशा में 3 घन्टे में तय करता है।

  1. Only I & II केवल I और II

  2. Only I & III केवल I और III

  3. All I, II & III सभी I, II और III

  4. Only II & III केवल II और III

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

From statement II: Downstream speed = 60 km/5 hr = 12 km/hr. From statement III: Downstream speed = y km/3 hr. For the same conditions, y/3 = 12, giving y = 36 km. We only need statements II & III; statement I (current speed) is irrelevant since we're dealing only with downstream motion in both cases.

Multiple choice

Each of given questions consists of a question followed by informations in three statements. You have to study the question and the statements and decide that information in which of the statement(s) is/are necessary to answer the question. find the speed of the man in still water? Statement I: A man can row 25 km upstream and 45 km downstream in 10 hours. Statement II: he can also travel 40 km in upstream and and 55 km downstream in 12 hours. Statement III: the distance travelled by man is same during upstream and downstream movement.

  1. Any two

  2. I and II

  3. I and II or III

  4. Only I

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

Let boat speed = b, stream speed = s. From I: 25/(b-s) + 45/(b+s) = 10. From II: 40/(b-s) + 55/(b+s) = 12. Let x = 1/(b-s) and y = 1/(b+s). Then 25x + 45y = 10 and 40x + 55y = 12. Solving gives x = 1/10, y = 1/15. So b-s = 10, b+s = 15, giving b = 12.5. Statement III is not needed as the equations from I and II are sufficient.

Multiple choice

The time taken by the boat in upstream is 2 hours while the time taken by the same boat to travel same distance in downstream is 1 hour and 30 minutes. The speed of the boat is 21 km/h. Then find how much distance boat will cover in upstream in 3 hours and 30 minutes? नाव द्वारा धरा के विरुद्ध में लिया गया समय 2 घंटे है जबकि उसी नाव द्वारा उतनी ही दूरी चलने के लिए धरा के साथ में लिया गया समय 1 घंटा 30 मिनट है। नाव की गति 21 किमी / घंटा है। फिर ज्ञात करें कि 3 घंटे और 30 मिनट में धरा के विरुद्ध नाव कितनी दूरी तय करेगी?

  1. 51.5 km 51.5 किमी

  2. 52.5 km 52.5 किमी

  3. 53.5 km 53.5 किमी

  4. 54.5 km 54.5 किमी

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

Let stream speed be s km/h. Boat speed = 21 km/h. Downstream speed = 21 + s, upstream speed = 21 - s. Upstream time = 2 hr, downstream time = 1.5 hr. Distance D = (21 - s) × 2 = (21 + s) × 1.5. Solving: 42 - 2s = 31.5 + 1.5s, giving 3.5s = 10.5, so s = 3 km/h. Upstream speed = 21 - 3 = 18 km/h. In 3.5 hours, distance = 18 × 3.5 = 63 km. This is not in options A-D, so E (None of these) is correct.

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 : Radha reaches her school from her house in 12 hours. If she increases her speed by 20% , then how long will she take to cover the same distance? Quantity II : Radha reaches her school from her house in 9 hours. If she decreases her speed by 10%, then how long will she take to cover the same distance? मात्रा I : राधा अपने घर से 12 घंटे में स्कूल पहुंचती है। यदि वह अपनी गति में 20% की वृद्धि करती है, तो वह उसी दूरी को तय करने में कितना समय लेगी? मात्रा II : राधा अपने घर से 9 घंटे में स्कूल पहुंचती है। यदि वह अपनी गति 10% कम कर देती है, तो वह समान दूरी तय करने में कितना समय लेगी?

  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
E Correct answer
Explanation

Quantity I: Original time = 12 hours. Speed increases by 20% (multiplied by 1.2), so new time = 12/1.2 = 10 hours. Quantity II: Original time = 9 hours. Speed decreases by 10% (multiplied by 0.9), so new time = 9/0.9 = 10 hours. Since both quantities equal 10, the relationship is equality. Option E is correct.