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

Distance between two places A and B is 266 km, a train leaves from A to B and simultaneously another train leaves from B to A and meet at the end in 14 hours. If the former trains travels 3 km faster than the other, then speed of train from B is.

  1. 12 km/h

  2. 6 km/h

  3. 8 km/h

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

Distance = 266 km, trains meet after 14 hours. Let slower train speed (from B) = x km/h, then faster train speed (from A) = (x+3) km/h. Relative speed = x + (x+3) = 2x + 3 km/h. Distance covered when they meet = 266 km. Time = 266 / (2x + 3) = 14 hours. So 266 = 14(2x + 3). 266 = 28x + 42. 28x = 224. x = 8 km/h. Therefore, train from B travels at 8 km/h.

Multiple choice

A train is moving at a speed of 160 km/h and covers a certain distance in 4.5 hours. Find the speed of the train to cover the same distance in 4 hours ? ( in km/hr )

  1. 120

  2. 180

  3. 170

  4. 175
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Distance = Speed × Time = 160 × 4.5 = 720 km. Speed needed to cover 720 km in 4 hours = 720/4 = 180 km/h. Speed and time are inversely proportional for fixed distance, so new speed = old speed × (old time/new time) = 160 × (4.5/4) = 180 km/h.

Multiple choice

A taxi driver leaves delhi at 7:30 am and expects to reach a place 500 km from delhi at 7:30 pm. At 12:30 he finds that he has covered only 30% of the distance. By how much he has to increase the speed of the taxi to reach his destination on time ?

  1. 25

  2. 50

  3. 30

  4. 20
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total time = 12 hours (7:30 am to 7:30 pm). Required speed = 500/12 = 41.67 km/h. By 12:30 pm (5 hours), only 30% (150 km) covered. Speed used = 150/5 = 30 km/h. Remaining 350 km in 7 hours needs speed = 350/7 = 50 km/h. Increase needed = 50 - 30 = 20 km/h, which is option D.

Multiple choice

A man completed a certain journey by train . if 25% of the distance is covered by 300 km/hr, 20% of the distance at 200 km/hr and remaining distance at 550 km/hr. Find the approximate average speed for the whole journey ?

  1. 350

  2. 351

  3. 353

  4. 359
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average speed = total distance / total time. Let distance be 100 km. Times: 25 km at 300 km/hr = 0.0833 hr, 20 km at 200 km/hr = 0.1 hr, 55 km at 550 km/hr = 0.1 hr. Total time = 0.2833 hr. Average speed = 100/0.2833 ≈ 353 km/hr.

Multiple choice

If the speed of a boat in still water is 25 km/hr and the speed of the current is 5 km/hr, then find the time taken by the boat to cover 135 km downstream.

  1. 5 hour and 30 minutes

  2. 4 hours

  3. 5 hours

  4. 4 hours and 30 minutes
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Downstream speed = boat speed + current speed = 25 + 5 = 30 km/hr. Time = distance/speed = 135/30 = 4.5 hours = 4 hours 30 minutes. Option A incorrectly adds time, B and C are calculation errors.

Multiple choice

A motor car starts with the speed of 70 km/hr with its speed increasing every two hours by 10 kmph. In how many hours will it cover 345 kms? एक मोटर कार 70 किमी./घंटा की चाल से चलना प्रारम्भ करती है और प्रत्येक दो घंटे में इसकी चाल 10 किमी./घंटा से बढ़ जाती है | कितने घंटों में यह 345 किमी. की दूरी तय करेगी ?

  1. 4 hours 4 घंटे

  2. 4 hours 5 minutes 4 घंटे 5 मिनट

  3. 4 hours 30 minutes 4 घंटे 30 मिनट

  4. 2 hours 2 मिनट

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

Speed starts at 70 km/h, increases by 10 km/h every 2 hours. First 2 hours: 70 km/h covers 140 km. Next 2 hours: 80 km/h covers 160 km. Total in 4 hours = 300 km. Remaining distance = 345 - 300 = 45 km. Speed for next 2 hours = 90 km/h, so 45 km takes 45/90 = 0.5 hours = 30 minutes. Total time = 4 hours 30 minutes.

Multiple choice

A man is standing at a distance of 360 metres from a hill. If he shouts, he hears the echo after 2.4 seconds. Then, what will be the speed of sound in air?
  1. $220 m/sec$
  2. $330 m/sec$
  3. $300 m/sec$
  4. $270 m/sec$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The echo travels from the person to the hill and back, covering twice the distance (720m total). Speed = Distance / Time = 720 / 2.4 = 300 m/sec. This is the standard calculation for echo-based speed of sound problems.

Multiple choice

A man crosses a river in a downstream through a 15 m long ship at the speed of 25 km/hr. If that man reaches one end of the river to another end in 1.5 hours, the river is flowing at the rate of 3km/hr the find the width of the river? एक आदमी , 25 किमी / घंटा की गति से चलते हुए 15 मीटर लंबे जहाज के माध्यम से एक नदी को धारा के अनुदिश पार करता है। यदि वह व्यक्ति 1.5 घंटे में नदी के एक छोर से दूसरे छोर तक पहुंच जाता है, जो 3 किमी / घंटा की दर से बह रही है तो नदी नदी की चौड़ाई ज्ञात कीजिए ?

  1. 42 Km 42 किमी

  2. 22 Km 22 किमी

  3. 33 km 33 किमी

  4. 42.03 km 42.03 किमी

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

If traveling downstream with current at 25+3 = 28 km/hr for 1.5 hours, distance = 42 km. But the question asks for river width, which is perpendicular to flow. The ship length (15m) is irrelevant and unit-inconsistent. Neither width nor crossing time can be determined from given data.

Multiple choice

For covering a distance P km, a man takes t hour. He takes 40 min less if he moves 3 km/hr. faster, But if he moves slower by 2 km/hr, he takes 40 min more. then P is equal to: P किमी. की दूरी तय करने में एक व्यक्ति को t घण्टे लगते हैं। यदि वह 3 किमी./घण्टे तेज चले तो 40 मिनट कम लगते हैं लेकिन यदि वह 2 किमी./घण्टा धीमे चले तो 40 मिनट अधिक लगते हैं तो P बराबर है-

  1. 20 km 20 किमी

  2. 30 km 30 किमी

  3. 40 km 40 किमी

  4. 45 km 45 किमी

  5. None of these तय नहीं कर सकते हैं
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let original speed be v km/hr, then P = vt. When speed increases by 3 km/hr: P/(v+3) = t - 2/3 hours. When speed decreases by 2 km/hr: P/(v-2) = t + 2/3 hours. Substituting P = vt and solving gives v = 12 km/hr, t = 10/3 hours, so P = 40 km. The key is converting 40 minutes to 2/3 hours and setting up the inverse relationship between speed and time.

Multiple choice

Speed of the boat is 16(2/3)% more than the speed of the car which moves 120 km at 4 hours. The boat covers a distance of 164 km downstream in 4 hrs. Find the distance covered by the boat upstream in 5 hrs.

  1. 110 km

  2. 160 km

  3. 130 km

  4. 150 km

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

Car speed = 120/4 = 30 km/h. Boat is 16(2/3)% more = 1/6 more, so boat speed = 35 km/h. Downstream: boat + stream = 164/4 = 41 km/h, so stream = 6 km/h. Upstream: boat - stream = 35 - 6 = 29 km/h. Distance in 5 hours = 29 × 5 = 145 km. None of the options (110, 160, 130, 150) match 145 km, so "None of these" is correct.

Multiple choice

A biker increases his speed by 10% after travelling for 1 hour every time. He covers 198.6 km in 3 hour. Average speed in last 2 hours (in km/hr) is?

  1. 58.4

  2. 66.6

  3. 69.3

  4. 63.8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial speed = v km/h. Hour 1: distance = v. Hour 2: speed = 1.1v, distance = 1.1v. Hour 3: speed = 1.21v, distance = 1.21v. Total: v + 1.1v + 1.21v = 3.31v = 198.6, so v = 60. Hour 2 speed = 66, Hour 3 speed = 72.6. Avg last 2 hrs = (66 + 72.6)/2 = 69.3 km/h. The progressive 10% increases create this average.

Multiple choice

The distance of the college and the home of Rajeev is 80 km. One day he was late by 1 hour than the normal time to leave for the college, so he increased his speed by 4 km/h and thus he reached to college at the normal time. What is the changed (or increased) speed of Rajeev?

  1. 16 km/h

  2. 30 km/h

  3. 40 km/h

  4. 20 km/h

  5. 15 km/hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let normal speed = v km/h, time = t hours. Distance = vt = 80. Late by 1 hour, new speed = v+4, time = t-1. Distance = (v+4)(t-1) = 80. Since vt = 80, we have vt + 4t - v - 4 = vt. 4t - v - 4 = 0. Also t = 80/v. Substitute: 4(80/v) - v - 4 = 0. 320/v - v - 4 = 0. Multiply by v: 320 - v² - 4v = 0. v² + 4v - 320 = 0. (v+20)(v-16) = 0. v = 16 (positive). New speed = v+4 = 20 km/h.

Multiple choice

A train started from station A and proceeded towards station B at a speed of 96 km/h. 45 minutes later, another train started from station B and proceeded towards station A at 100 km/h. If the distance between the two stations is 856 km, at what distance from station A will the trains meet?.

  1. 456 km

  2. 588 km

  3. 528 km

  4. 800 Km

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

First train travels for 45 minutes (0.75 hours) alone: distance = 96 × 0.75 = 72 km from A. Remaining distance = 856 - 72 = 784 km. When both trains move toward each other, relative speed = 96 + 100 = 196 km/h. Time to meet = 784 ÷ 196 = 4 hours. In this time, first train covers additional 96 × 4 = 384 km. Total from A = 72 + 384 = 456 km. Option B (588) incorrectly uses only the relative speed portion.