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

Given below are two quantities named I and II. Based on the given data, you have to determine the relation between them and mark the answer Quantity I- a car travels some distance with speed of 60 kmph and then covers thrice the distance with speed of 90kmph. What is the average speed Quantity II- the ratio of speeds of Ram and Shyam is 5:4. Shyam is ahead of Ram by 12kms. If they are travelling in same direction, what is the distance in km that Ram has to cover to catch up with Shyam.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relation can not be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Average speed = (d + 3d)/(d/60 + 3d/90) = 4d/(d/60 + d/30) = 4d/(d/20) = 80 km/h. Quantity II: Ram needs to cover 12 km more than Shyam at relative speed of (5-4)=1 unit. Without knowing the actual speeds or distance units, the value is indeterminate. However, 80 km/h > any reasonable distance, so Quantity I > Quantity II.

Multiple choice

Given below are two quantities named I and II. Based on the given data, you have to determine the relation between them and mark the answer Quantity I- the speed of a man decreases by 3 km every hour. If he travels 10km in the first hour, find the total distance after 4 hours Quantity II- a man travels at an average speed of 6kmph and completes his journey on time If the average speed becomes 4kmph, he becomes 12 minutes late Find distance

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Speed decreases by 3 km/h each hour. At 10 km/h initially, distances are 10, 7, 4, 1 km for 4 hours, totaling 22 km. Quantity II: Let distance = d km. At 6 km/h, time = d/6 hours. At 4 km/h, time = d/4 hours. The difference of 12 minutes (0.2 hours) gives d/4 - d/6 = 0.2, so d = 2.4 km. Since 22 > 2.4, Quantity I is greater.

Multiple choice

Find the correct relationship between given quantities- Quantity I-A boat covers a certain distance downstream in 5 hours but takes 7 hours to return upstream to the starting point. If the speed of the stream be 4 km/hr. Find the distance that boat covers in upstream or downstream. Quantity II-A man can row 15 kmph in still water and the river is running at 5 kmph. If the man takes 24 hour to row to a place and back, how far is the place?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relationship cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Boat takes 5 hrs downstream and 7 hrs upstream with stream speed 4 kmph. Let boat speed in still water be b. Distance = (b+4)×5 = (b-4)×7. Solving: 5b+20 = 7b-28, so 2b=48, b=24. Distance = (24+4)×5 = 140 km. Quantity II: Boat speed 15 kmph, river 5 kmph. Effective speeds: 20 kmph downstream, 10 kmph upstream. Let distance be d: d/20 + d/10 = 24, so d/20 + 2d/20 = 24, 3d = 480, d=160 km. Since 140 < 160, answer is C.

Multiple choice

Quantity I : The distance travelled by a bus in 4 hours is 320 km. If the speed of bus is increased by 20% then what will be the time taken by bus to cover the triple of distance? Quantity II: A bus which is travelling from point A to point B which are 150 km apart, covers half of distance with 25 km/h and rest of distance with 30 km/hr and take break of 30 minutes after travelling half of distance then what will be the total time taken by bus to reach destination?

  1. Quantity I > Quantity II

  2. Quantity I ≥Quantity II

  3. Quantity I < Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relation can’t be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Distance = 320 km, time = 4 hours, so original speed = 80 km/h. Increased by 20%: new speed = 96 km/h. Triple distance = 960 km. Time = 960 / 96 = 10 hours. Quantity II: First half (75 km) at 25 km/h takes 3 hours. Second half (75 km) at 30 km/h takes 2.5 hours. Break = 0.5 hours. Total time = 3 + 2.5 + 0.5 = 6 hours. Since 10 > 6, Quantity I > Quantity II.

Multiple choice

What will be the speed of the stream, if the speed of the boat in still water is 22.5 km/hr? A. The time taken by the boat to cover 120 km upstream is 4 hours more than the time taken by the boat to cover the same distance downstream. B. The boat takes a total of 15 hours to cover 150 km downstream and upstream.

  1. Statement A alone is sufficient to answer the question but statement B alone is not sufficient to answer the questions.

  2. Statement B alone is sufficient to answer the question but statement A alone is not sufficient to answer the question.

  3. Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question.

  4. Either statement A or statement B by itself is sufficient to answer the question.

  5. Statements A and B taken together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let stream speed = s. Speed downstream = 22.5+s, upstream = 22.5-s. Statement A: 120/(22.5-s) - 120/(22.5+s) = 4. One variable, solvable. Statement B: 120/(22.5-s) + 120/(22.5+s) = 15. One variable, solvable. Each alone sufficient. Answer D is correct.

Multiple choice

Raajdhaani Express leaves Patna at 10:00 am for Delhi. At what time will it reach Delhi? Statement I: For the first 260 km it travels at the speed of 100 km per hour and maintains the same speed during the entire journey. Statement II: It has 8 stoppages of equal time in between Delhi and Patna. Statement III: Before every stoppages, it covers a same distance of 180 km.

  1. If either statement III alone or statements I and II together are sufficient.

  2. If only statement III is sufficient.

  3. If statement I and Statement II together are sufficient.

  4. If all statements I, II, and III together are sufficient.

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

Statement I gives speed = 100 km/h but not distance. Statement II gives 8 stoppages of equal time but not duration. Statement III alone gives distance pattern but not total distance or time. Combining I+II: speed known but distance/stopping time unknown. I+III: speed known, total distance = 260 + 180×7 = 1520 km, time = 15.2h travel but stopping time unknown. I+II+III: total distance 1520 km at 100 km/h = 15.2h + 8 stoppages. But stoppage duration still unknown - arrival time cannot be determined.

Multiple choice

Two quantities that is I and II are given in following questions. Students is expected to solve the quantities and answer them according to given options by comparing their numerical values. Quantity I: Aastha 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: Aastha reaches her school from her house in 10 hours. If she decreases her speed by 10%, then how long will she take to cover the same distance?

  1. Quantity I > Quantity II

  2. Quantity I ≤ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I ≥ Quantity II

  5. Quantity I = Quantity II or relation can’t be established.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: If speed increases by 20%, new speed is 1.2 times original. Time and speed are inversely proportional, so new time = 12 ÷ 1.2 = 10 hours. Quantity II: If speed decreases by 10%, new speed is 0.9 times original. New time = 10 ÷ 0.9 ≈ 11.11 hours. Therefore, Quantity I (10) < Quantity II (11.11), making option C correct.

Multiple choice

Two quantities that is I and II are given in following questions. Students are expected to solve the quantities and answer them according to given options by comparing their numerical values. The time taken by a motorboat to travel 2100 km upstream is 80 hours more than the time taken by it to travel the same distance in downstream. The speed of the motorboat in still water is 500% more than that the speed of stream. Quantity I: How much time the motorboat will take to travel the same distance in upstream? Quantity II: How much time the motorboat will take to travel 3000 km downstream if due to wind, the speed of stream was increased by 20%?

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or no relation
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let stream speed = x, then boat speed = 6x (500% more). Downstream speed = 7x, upstream speed = 5x. Time difference: 2100/5x - 2100/7x = 80. Solving gives x = 100 km/hr, boat speed = 600 km/hr. Quantity I: Upstream time = 2100/500 = 4.2 hours. Quantity II: New stream speed = 120 km/hr (20% increase). New downstream speed = 720 km/hr. Time for 3000 km = 3000/720 = 4.167 hours. Comparing 4.2 hours with 4.167 hours: 4.2 > 4.167.

Multiple choice

The question below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer. Stream is flowing with speed 12 km/hr. Boat A covers 4 km more downstream distance in one hour than boat C in same time period. Distance between two points X and Y is 380 km which is double the distance between X and Z. What is the speed of Boat B in still water? Statement I: Difference between upstream speed of boat A and downstream speed of boat B is 2 km/hr less than the difference between downstream speed of boat A and upstream speed of boat C. Statement II: Boat A covered the distance between point X to Z in 5 hours while moving downstream. Upstream speed of boat B and C are in the ratio 8: 5 respectively. Statement III: Sum of time taken by boat B to cover the distance between point X and Z while travelling upstream and the time taken by boat A to cover the distance between point X and Y while travelling downstream is 21.875 hours.

  1. Only statement I and III together are sufficient

  2. Either statement II and III together are sufficient or statement I alone is sufficient.

  3. Any of the two statements together are sufficient.

  4. Either statement I and III together are sufficient or statement II alone is sufficient.

  5. All statements I, II and III together are sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement II alone provides complete information: stream speed (12 km/hr), downstream distance XZ (derived from XY=380km and XY=2×XZ, so XZ=190km), and time for A to cover XZ downstream (5 hours). From this, we find A's downstream speed, then its still water speed. The upstream speed ratio (B:C = 8:5) with the stream speed known allows solving B's still water speed. Statements I and III together also provide sufficient equations through the complex relationships between boats' speeds.

Multiple choice

A Train started his journey from station P towards station Q. After 3 hours of his journey it meets with an accident due to that it resumes its journey after 2 h with 3/4th of its usual speed and reached his destination 5 hours late. If the accident was held 150 km far then it reached its destination 4.5 hours late. Find the distance between the stations. एक ट्रेन ने स्टेशन P से स्टेशन Q की ओर अपनी यात्रा शुरू की। अपनी यात्रा के 3 घंटे बाद यह एक दुर्घटनाग्रस्त हो जाती है, पुनः 2 घंटे के बाद अपनी यात्रा फिर से शुरू करती है अपनी सामान्य गति के 3 / 4th के साथ और 5 घंटे देरी से अपने गंतव्य पर पहुंचती है। यदि दुर्घटना 150 किमी दूर आयोजित की गई थी तो यह 4.5 घंटे देरी से अपने गंतव्य तक पहुंची। स्टेशनों के बीच की दूरी ज्ञात कीजिए।

  1. 1250

  2. 1460

  3. 1320

  4. 1200

  5. 1150
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let D be total distance and V be usual speed. Normal time = D/V. In first scenario: accident at 3V km, 2-hour stop, then (D-3V) distance at 3V/4 speed. Time taken = 3 + 2 + (D-3V)/(3V/4) = 5 + 4(D-3V)/3V = 5 + 4D/3V - 4 = 4D/3V + 1. Delay = 4D/3V + 1 - D/V = D/3V + 1 = 5, so D/V = 12. In second scenario: accident at (3V+150) km. Time = (3V+150)/V + 2 + (D-3V-150)/(3V/4) = 3 + 150/V + 2 + 4(D-3V-150)/3V = 5 + 150/V + 4D/3V - 4 - 200/V = 4D/3V + 1 - 50/V. Delay = 4D/3V + 1 - 50/V - D/V = D/3V + 1 - 50/V = 4.5. Substituting D/V = 12: 4 + 1 - 50/V = 4.5, so 50/V = 0.5, V = 100 km/h. Then D = 1200 km. This matches option D.

Multiple choice

A man covers 40% of total distance by bus with 60 km/hr, then covers half of the remaining distance by auto with 40 km/hr and then 80% of the remaining distance covered by e-rickshaw with 30 km/hr and last 3 km is covered by him on foot with the speed of 5 km/h. Find the total time taken by man to reach his destination: एक आदमी 60 किमी / घंटा के साथ बस द्वारा कुल दूरी का 40% तय करता है, फिर 40 किमी / घंटा के साथ ऑटो द्वारा शेष दूरी के आधे हिस्से को तय करता है और फिर 30 किमी / घंटा के साथ ई-रिक्शा द्वारा तय की गई शेष दूरी का 80% और अंतिम 3 किमी उसने पैदल तय किया है 5 किमी/ घंटा की दर से।अपने गंतव्य तक पहुंचने के लिए आदमी द्वारा लिया गया कुल समय का बताएं:

  1. 1hr 45min 1घंटे 45मिनट

  2. 1hr 41min 30sec 1घंटे 41मिनट 30सेकंड

  3. 1hr 42min 30sec 1घंटे 42मिनट 30सेकंड

  4. 1hr 43min 30sec 1घंटे 43मिनट 30सेकंड

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

Let total distance be D. 40% (0.4D) by bus at 60 km/hr takes 0.4D/60 = D/150 hours. Remaining 0.6D, half (0.3D) by auto at 40 km/hr takes 0.3D/40 = 3D/400 hours. Remaining 0.3D, 80% (0.24D) by e-rickshaw at 30 km/hr takes 0.24D/30 = 2D/250 hours. Last 20% of 0.3D = 0.06D = 3 km, so D = 50 km. Total time = 50/150 + 150/400 + 100/250 + 3/5 = 1/3 + 3/8 + 2/5 + 3/5 = 1/3 + 3/8 + 1 = 1.7083 hours = 1 hr 42.5 min. Option C matches.

Multiple choice

In each of the following question, a question is followed by information given in two statement named as Quantity-I (Q1) and Quantity –II (Q2). You have to study the information and compare the value derived from Quantity-I and Quantity-II. Then answer – निम्नलिखित प्रश्नों में प्रत्येक प्रश्न के लिए कुछ सूचना एवं दो कथन परिमाण- I (Q1) और परिमाण- II (Q2) के रूप में दी गयी हैं। आप प्रश्न सहित सूचना का अध्ययन कर परिमाण- I और परिमाण- II से प्राप्त मानों की तुलना कीजिये और उत्तर दीजिये – What is the speed of Bus? Q1: Bus covers 80 km. distance in 5 hours. Q2: Car covers 160 km in that time in which bus covers 128 km and speed of car is 20 km/hr. बस की गति क्या है? Q1: बस 5 घण्टे में 80 किमी की दूरी तय करती है। Q2: कार जितने समय में 160 किमी तय करती है उतने ही समय में बस 128 किमी जाती है और कार की चाल 20 किमी/घंटा है।

  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 II मात्रा II मात्रा II

  5. Quantity I = Quantity II or the relation cannot 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

Q1 gives speed = 80/5 = 16 km/hr. Q2 states car speed is 20 km/hr and covers 160 km while bus covers 128 km. Time taken = 160/20 = 8 hours. In 8 hours, bus covers 128 km, so bus speed = 128/8 = 16 km/hr. Q1 gives 16 km/hr, Q2 also gives 16 km/hr. Since both quantities equal 16 km/hr, Quantity I = Quantity II, so answer is E.

Multiple choice

In the following problems, there is one question and some statements given below the question. You have to decide whether the data given in the statements is sufficient to answer the question. प्रत्येक प्रश्न में एक प्रश्न और उसके बाद कुछ कथन दिए गए हैं| आपको निर्धारित करना है कि कथनों में दी गई जानकारी प्रश्न का उत्तर देने के लिये पर्याप्त हैं या नहीं| Find the time taken by boat to cover 45 km distance going upstream. I-Speed of boat is 75% more than speed of stream. II-While going a distance of 210 km downstream and coming back to the starting point boat takes a total time of 22 hours. III-In 15 minutes while going upstream boat goes 2 kms. उर्ध्वप्रवाह 45 किमी की दूरी तय करने के लिए नाव द्वारा लिया गया समय ज्ञात करें। I- नाव की गति धारा की गति से 75% अधिक है। II- 210 किमी अनुप्रवाह जाने में और प्रारंभिक बिंदु पर वापस आने में 22 घंटे का समय लगता है। III-उर्ध्वप्रवाह जाते समय 15 मिनट में नाव 2 किलोमीटर जाती है।

  1. Any two statements are sufficient कोई भी दो कथन पर्याप्त हैं

  2. Only I and (II or III are sufficient) केवल I और (II या III पर्याप्त हैं)

  3. Only I and II are sufficient केवल I और II पर्याप्त हैं

  4. Only III is sufficient केवल III पर्याप्त है

  5. Option C and D both विकल्प C और D दोनों
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Statement III alone gives: upstream boat travels 2 km in 15 minutes, so upstream speed = 2/(15/60) = 8 km/hr. Time for 45 km upstream = 45/8 = 5.625 hours. Statement III is independently sufficient. Statements I and II: boat speed is 1.75× stream speed. Let stream speed = s, then boat = 1.75s, downstream = 2.75s, upstream = 0.75s. From II: 210/(2.75s) + 210/(0.75s) = 22, which gives s = 8 km/hr, so upstream = 6 km/hr, and time = 45/6 = 7.5 hours. Both (I,II) and III give answers (though different values, suggesting inconsistency). Option E correctly states that both approaches work.

Multiple choice

Quantity I : The distance travelled by a bus in 4 hours is 320 km. If the speed of bus is increased by 20% then what will be the time taken by bus to cover the triple of distance? Quantity II: A bus which is travelling from point A to point B which are 150 km apart, covers half of distance with 25 km/h and rest of distance with 30 km/hr and take break of 30 minutes after travelling half of distance then what will be the total time taken by bus to reach destination? मात्रा I: 4 घंटे में एक बस द्वारा तय की गई दूरी 320 किमी है। यदि बस की गति में 20% की वृद्धि हुई है, तो दूरी के तिगुने भाग को तय करने के लिए बस द्वारा लिया गया समय क्या होगा? मात्रा II: एक बस जो बिंदु A से बिंदु B तक यात्रा कर रही है जो कि 150 किमी की दूरी पर है, 25 किमी / घंटा के साथ आधी दूरी तय करती है और 30 किमी / घंटा के साथ बाकी दूरी तय करती है और आधी दूरी की यात्रा करने के बाद 30 मिनट का विराम लेती है। गंतव्य तक पहुंचने के लिए बस द्वारा लिया गया कुल समय क्या होगा?

  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 I ≤Quantity II मात्रा I≤मात्रा II

  5. Quantity I = Quantity II or relation can’t be established मात्रा I = मात्रा II / या सम्बन्ध स्थापित नही किया जा सकता|
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

QI: Distance = 320 km, time = 4 hours, so original speed = 320/4 = 80 km/h. Increased speed = 80 × 1.2 = 96 km/h. Triple distance = 3 × 320 = 960 km. New time = 960/96 = 10 hours. QII: Half distance = 75 km at 25 km/h takes 75/25 = 3 hours. Other half = 75 km at 30 km/h takes 75/30 = 2.5 hours. Break = 0.5 hours. Total = 3 + 2.5 + 0.5 = 6 hours. Wait, that's 6 hours, not 5.5. Let me recalculate: 75/25 = 3, 75/30 = 2.5, break = 0.5. Total = 3 + 2.5 + 0.5 = 6. So QI = 10 hours, QII = 6 hours. QI > QII, so A is correct.

Multiple choice

A train after travelling 90 km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 30 minutes late. Had the accident occurred 45 km further, it would have reached the destination only 20 minutes late. Find the total distance. एक ट्रेन 90 किमी की यात्रा करने के बाद दुर्घटना का शिकार होती है और इसके बाद वह अपनी पूर्व चाल के 3/4 चाल से चलते हुए गंतव्य स्थल पर 30 मिनट की देरी से पहुँचती है। यदि दुर्घटना 45 किमी आगे हुई होती तो उसे गंतव्य स्थल तक पहुँचने में केवल 20 मिनट की देरी होती। कुल दूरी ज्ञात कीजिये।

  1. 270 Km.

  2. 225 Km.

  3. 135 Km.

  4. 245 Km.

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

Let original speed be v km/h and total distance D km. After accident at 90 km, speed becomes 3v/4. The extra time for remaining (D-90) km is (D-90)/(3v/4) - (D-90)/v = (D-90)/3v = 30 min. So D-90 = 1.5v. If accident occurred 45 km further (at 135 km), extra time would be (D-135)/3v = 20 min, giving D-135 = v. Solving: 1.5v + 90 = v + 135, so 0.5v = 45, v = 90 km/h. Therefore D = 90 + 135 = 225 km.