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

A cyclist completes a certain journey in 7 hours. He covers half the distance at 12 km./hr and the second half of the distance at 9 km/hr. The distance (in km) covered by the cyclist is- एक साइकिल सवार कोई यात्रा 7 घंटे में पूरी करता है। वह आधी दूरी 12 किमी/घं. की चाल से तथा शेष आधी दूरी 9 किमी/घं की चाल से चलता है। साइकिल सवार द्वारा चली गई दूरी है (किमी. मे ) -

  1. 72

  2. 36

  3. 108

  4. 180
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let total distance be d km. Time for first half = (d/2)/12 = d/24 hours. Time for second half = (d/2)/9 = d/18 hours. Total time: d/24 + d/18 = 7 hours. d(1/24 + 1/18) = 7, so d(7/72) = 7, giving d = 72 km. The harmonic mean of speeds for equal distances gives average speed = 2*12*9/(12+9) = 72/7 km/h. Distance = average speed × time = (72/7) × 7 = 72 km.

Multiple choice

A boat can cover X km while going downstream in same time in which it can cover (X-8) km while going up stream. If the difference between the distance covered in 1 hr. Downstream and upstream is 6 km and speed of boat in still water is 15 km/hr, then find the value of X.

  1. 12 km

  2. 16 km

  3. 20 km

  4. 24 km

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let stream speed = s km/hr. Downstream speed = 15+s, upstream = 15-s. In equal time t: distance downstream = (15+s)t = X, distance upstream = (15-s)t = X-8. Difference in 1 hour: (15+s) - (15-s) = 2s = 6, so s = 3. From the equations: X/(15+3) = (X-8)/(15-3), giving X/18 = (X-8)/12. Cross-multiply: 12X = 18X - 144, so 6X = 144, X = 24 km.

Multiple choice

A person covers half his journey by train at 60 km/hr, half the remainder by bus at 30 km/hr and the rest by cycle at 10 km/hr. Find his average speed during the entire journey. एक व्यक्ति अपनी आधी यात्रा ट्रेन से 60 किमी/घं., शेष की आधी यात्रा बस से 30 किमी/घं. और शेष साइकिल से 10 किमी/घं. की दर से तय की। तो पूरी यात्रा में उसकी औसत चाल क्या थी?

  1. 20 km/hr/किमी/घं.

  2. 12 km/hr/किमी/घं.

  3. 24 km/hr/किमी/घं.

  4. 18 km/hr/किमी/घं.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average speed = total distance / total time. Let total distance = 4d. Half journey (2d) by train at 60 km/h: time = 2d/60. Half of remainder (d) by bus at 30 km/h: time = d/30. Remaining (d) by cycle at 10 km/h: time = d/10. Total time = d(1/30+1/30+1/10) = d(2/30+3/30) = 5d/30 = d/6. Average speed = 4d/(d/6) = 24 km/h.

Multiple choice

In covering a distance of 30 km., Abhay takes 2 hours more than Sameer. If Abhay doubles his speed ,then he would take 1 hours less than Sameer .Abhay's speed (in km/hr.) is - 30 किमी. की दूरी तय करने में अभय, समीर से 2 घंटे अधिक समय लेता हैं यदि अभय अपनी चाल को दोगुना कर दे तो वह समीर से एक घंटा कम समय लेगा। अभय की चाल (किमी/घंटा) में है-

  1. 5

  2. 6

  3. 6.25

  4. 7.5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let Sameer's time be t hours. Abhay's time = t+2 hours. Sameer's speed = 30/t, Abhay's speed = 30/(t+2). When Abhay doubles speed: 60/(t+2) = t-1 (1 hour less than Sameer). Cross-multiplying: 60 = (t+2)(t-1) = t²+t-2. So t²+t-62=0. Solving: t = [-1±√(1+248)]/2 = [-1±√249]/2 ≈ 7.39. Abhay's speed = 30/(9.39) ≈ 3.2, which doesn't match. Let me redo: if Abhay takes 2 hours more, and doubling makes him take 1 hour less, then original: t+2, new: 2×30/(t+2) = 30/(t-1). Solving gives t=6, Abhay's speed = 30/8=3.75, still not matching options. The correct approach: let Abhay's speed = v, then 30/v = 30/s + 2 and 30/(2v) = 30/s - 1. This gives v=5 km/h.

Multiple choice

A train had to cover a distance of 46 km. between two stations. If it covers 25 km. at the speed of 40 kmph then at what speed it must travel the remaining distance? एक ट्रेन को दो स्टेशनों के बीच की दूरी 46 किमी. को एक घंटा में तय करना है यदि वह 25 किमी. दूरी तक 40 किमी./घंटा की चाल से चलती है तो उसको शेष दूरी किस चाल से तय करनी चाहिए ?

  1. 40 kmph/किमी./घंटा

  2. 50 kmph/किमी./घंटा

  3. 56 kmph/किमी./घंटा

  4. 72 kmph/किमी./घंटा
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total distance = 46 km, total time = 1 hour. Distance covered in first part = 25 km at 40 kmph. Time taken = 25/40 = 5/8 hour = 37.5 minutes. Remaining time = 60 - 37.5 = 22.5 minutes = 0.375 hours. Remaining distance = 46 - 25 = 21 km. Required speed = 21/0.375 = 56 kmph. Therefore, the train must travel at 56 kmph for the remaining distance.

Multiple choice

Sweta swims a certain distance down stream in 4 hours and she returns the same distance upstream in 6 hours. If the speed of current is 2 kmph, then find her speed of swimming upstream the current. श्वेता एक निश्चित दूरी धारा के अनुप्रवाह 4 घण्टे में तय करती है और वह उसी दूरी को धारा के ऊर्ध्वप्रवाह 6 घंटे में तय करती है। यदि धारा की चाल 2 किमी/घंटा है, तो धारा के ऊर्ध्वप्रवाह उसकी चाल ज्ञात कीजिए।

  1. 10 kmph/किमी/घंटा

  2. 8 kmph/किमी/घंटा

  3. 6 kmph/किमी/घंटा

  4. 12 kmph/किमी/घंटा
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let swimming speed in still water be v kmph. Downstream speed = v+2, upstream speed = v-2. Distance is same, so 4(v+2) = 6(v-2). Solving: 4v+8 = 6v-12, so 2v = 20, giving v = 10 kmph. The question asks for upstream speed, which is v-2 = 10-2 = 8 kmph. Answer is 8 kmph, which is option B.

Multiple choice

If a boat can travel a certain distance downstream in t1 hours and the same distance upstream in t2 hours then what is the speed of the current if the speed of the boat is 10 kmph. It is given that t2 is 50% more than that of t1?

  1. 1.5 kmph

  2. 2 kmph

  3. 2.5 kmph

  4. 3 kmph
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let current speed be x. Downstream speed = 10+x, upstream = 10-x. Given t2 = 1.5*t1, so (d/(10-x)) = 1.5*(d/(10+x)). Solving: 10+x = 1.5(10-x), giving x = 2 kmph.

Multiple choice

A boat running upstream takes 5 hours and 40 minutes to cover a certain distance, while it takes 3 hours to cover the same distance downstream. What is the ratio between the speed of current and speed of boat respectively? एक निश्चित दूरी को धारा के ऊर्ध्वप्रवाह तय करने में एक नाव 5 घंटे 40 मिनट लेती है, जबकि यह इस दूरी को धारा के अनुप्रवाह तय करने में 3 घंटे का समय लेती है। धारा की चाल और नाव की चाल में क्रमशः क्या अनुपात है?

  1. 20 : 1

  2. 4 : 13

  3. 13 : 4

  4. 19 : 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let distance = D. Upstream speed = D/(17/3) = 3D/17. Downstream speed = D/3. Boat speed = (upstream + downstream)/2 = (3D/17 + D/3)/2. Current speed = (downstream - upstream)/2. Ratio current:boat = (1/3 - 3/17):(1/3 + 3/17) = 4:13. Option B is correct.

Multiple choice

A person has to travel a distance in certain time. Travelling at a speed of 5 km/h he reaches 18 minutes late and while travelling at a speed of 8 km/h he reaches 9 minutes early.Find the total distance. किसी व्यक्ति को निश्चित समय में कुछ दूरी तय करनी है। 5 किमी / घंटा की गति से यात्रा करते हुए वह 18 मिनट देर से पहुंचता है और 8 किमी / घंटा की गति से यात्रा करते हुए वह 9 मिनट पहले पहुंचता हैं । कुल ज्ञात कीजिये |

  1. 5 km./किमी.

  2. 7.5 km./किमी.

  3. 6 km./किमी.

  4. 12 km./किमी.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let correct time = t, distance = d. At 5 km/h: t + 18/60 = d/5. At 8 km/h: t - 9/60 = d/8. Subtract: (d/5 - d/8) = 27/60. d(3/40) = 9/20. d = (9/20)×(40/3) = 6 km. The time difference between early and late arrival is 27 minutes total (18+9).

Multiple choice

A 110 m long train is running at the speed of 60 km/hr. In what time will it cross another 170 m long train standing on a parallel railway track?

  1. 15.6 sec.

  2. 16.8 sec.

  3. 17.2 sec.

  4. 18 sec.

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

When a moving train crosses a stationary object, the distance covered equals the sum of their lengths. Total distance = 110m + 170m = 280m. Convert speed: 60 km/hr = 60 × (5/18) m/s = 50/3 m/s. Time = Distance/Speed = 280 ÷ (50/3) = 280 × 3/50 = 16.8 seconds. Option B is correct. Option A (15.6s) and C (17.2s) are calculation errors, while D (18s) ignores precise conversion.

Multiple choice

A motorcyclist covered two-thirds of a total journey at his usual speed. He covered the remaining distance at three-fourth of his usual speed. As a result he arrived 30 min later than the time he would have taken at usual speed. If the total journey was 180 km, then what is his usual speed?

  1. 40 km/h

  2. 36 km/h

  3. 30 km/h

  4. 32 km/h
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let usual speed = v. Distance = 180 km. Time at usual speed = 180/v hours. Actual time: (120/v) + (60/(3v/4)) = 120/v + 80/v = 200/v hours. Delay = 200/v - 180/v = 20/v hours = 30 minutes. So 20/v = 0.5, giving v = 40 km/h.

Multiple choice

A bus covers a certain distance in 12 hour. If the speed of bus in increased by 10 km. /hr., the same distance would have been covered in 10 hr. Find the distance covered. एक बस किसी दूरी को 12 घण्टे में तय करती है। यदि बस की चाल 10 किमी./घण्टे बढ़ा दी जाय तो अब बस वही दूरी 10 घण्टे में तय करती है । बस द्वारा तय की गयी दूरी ज्ञात करें ।

  1. 480 Km/किमी

  2. 600 Km/किमी

  3. 720 Km/किमी

  4. 800 Km/किमी
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the original speed be v km/hr. Distance = speed × time, so d = 12v. When speed increases by 10 km/hr, the same distance is covered in 10 hours: d = 10(v+10). Equating: 12v = 10v + 100, so v = 50 km/hr. Distance = 12 × 50 = 600 km.

Multiple choice

A man goes downstream with a boat to some destination and returns upstream to his original place in 5 hours. If the speed of boat in still water and the stream are 10 km/hr. and 4 km/hr. respectively, the distance of the destination from the starting place is - एक व्यक्ति नाव से धारा की दिशा में किसी स्थान पर जाता है और पुनः धारा के प्रतिकूल दिशा में अपने नियत स्थान पर 5 घंटे में वापस आ जाता है। यदि शान्त जल में नाव की चाल तथा धारा की चाल क्रमशः 10 किमी./घंटा तथा 4 किमी. घंटा है, तो प्रारम्भिक बिन्दु से उस स्थान की दूरी क्या है?

  1. 16 km/किमी.

  2. 18 km/किमी.

  3. 21 km/किमी.

  4. 25 km/किमी.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Downstream speed = 10+4 = 14 kmph. Upstream speed = 10-4 = 6 kmph. Let distance = D. Total time = D/14 + D/6 = 5 hours. D(1/14 + 1/6) = 5. D(4/84 + 14/84) = 5. D(18/84) = 5. D = 5×84/18 = 420/18 = 21 km.

Multiple choice

A man rides at the rate of 18 km/hr, but stops for 6 min. to change horses at the end of every 7th km. finds the time he will take to cover a distance of 90 km.

  1. 6 hrs.

  2. 6 hrs. 18 min

  3. 6 hrs. 12 min

  4. 6 hrs. 24 min
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The rider covers 90 km at 18 km/hr, taking 5 hours of riding time (90/18 = 5). There are 12 complete segments of 7 km each (7 × 12 = 84 km) with 6 km remaining. The rider stops after every 7th km, which means 12 stops of 6 minutes each, totaling 72 minutes (1 hour 12 minutes). Total time = 5 hours + 1 hour 12 minutes = 6 hours 12 minutes.