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

Two cyclists, Amit and Bimal, participate in a 50 kilometre race. Amit starts the cycling at a constant speed of 12 kilometres per hour. After 30 minutes, Bimal starts cycling at a constant speed of 15 kilometres per hour. What is the distance from the starting point where Bimal will meet Amit?

  1. 20 km

  2. 30 km

  3. 35 km

  4. 40 km

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

Amit travels for 0.5 hours at 12 km/h, covering 6 km before Bimal starts. The relative speed of Bimal to Amit is 15 - 12 = 3 km/h. Bimal needs 6 km / 3 km/h = 2 hours to catch up to Amit. In these 2 hours, Bimal travels 15 km/h * 2 hours = 30 km.

Multiple choice

Two cyclists, Peter and Sarah, start cycling toward each other from two different points, Point A and Point B, which are 100 kilometers apart. Peter cycles at a speed of 20 km/h for the first 40 kilometers, and then increases his speed to 25 km/h for the remaining distance. Sarah cycles at a constant speed of 15 km/h throughout. How long will it take for Peter and Sarah to meet each other?

  1. 2 hours and 45 minutes

  2. 3 hours and 15 minutes

  3. 3 hours and 45 minutes

  4. 4 hours and 15 minutes

  5. 4 hours and 45 minutes
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Two cars, Car A and Car B, start from opposite points at the same time. The speeds of both cars form a geometric progression (GP). Car A starts with a speed of 80 km/h, while Car B starts with a speed of 88 km/h. Each subsequent hour, the speed of both the cars decreases by a factor of 0.5. If the distance between the starting points of Car A and Car B is 315 kilometres, find the time it takes for them to meet.

  1. 4 hours

  2. 6 hours

  3. 8 hours

  4. They never meet.

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

Speeds form a GP with r = 0.5. Speed of A at hour n: 80 * (0.5)^(n-1). Speed of B at hour n: 88 * (0.5)^(n-1). Sum of distances covered in 4 hours: Sum = (a(1-r^n))/(1-r). For A: 80(1-0.5^4)/(1-0.5) = 160(0.9375) = 150. For B: 88(1-0.5^4)/(1-0.5) = 176(0.9375) = 165. Total distance = 150 + 165 = 315.

Multiple choice

A runner started a race at 9 a.m. and ran at a speed of 12 km/h. After completing the race, the runner rested for 20 minutes and then ran back to the starting point at a speed of 18 km/h. The runner reached the starting point at 11.05 a.m. Calculate the total distance covered by the runner during the race.

  1. 63 km

  2. 13 km

  3. 12.6 km

  4. 13.6 km

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

Let the one-way distance be d km. The running time is d/12 + d/18 hours, and the total elapsed time excluding the 20-minute rest is 1 hour 45 minutes, or 1.75 hours. Solving gives d × 5/36 = 1.75, so d = 12.6 km.

Multiple choice

In a city, there are three types of vehicles: cars, motorcycles, and bicycles. The total number of vehicles is 510. The ratio of cars to motorcycles is 3 : 5, and the ratio of motorcycles to bicycles is 2 : 7. If 40% of the cars, 25% of the motorcycles, and 16% of the bicycles are electric vehicles and run with an average speed of 30 km/h, and the remaining vehicles are conventional and run with average speeds of 60 km/h (cars), 80 km/h (motorcycles), and 20 km/h (bicycles), what is the total distance covered by all vehicles in one hour?

  1. 17,190 km

  2. 15,670 km

  3. 12,865 km

  4. 8,970 km

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

Total vehicles = 510. Ratios: C:M = 3:5, M:B = 2:7. C:M:B = 6:10:35. Total parts = 51. Each part = 10. Cars = 60, Motorcycles = 100, Bicycles = 350. Electric: 0.4*60=24, 0.25*100=25, 0.16*350=56. Conventional: 36, 75, 294. Distance = (24+25+56)*30 + (36*60 + 75*80 + 294*20) = 105*30 + 2160 + 6000 + 5880 = 3150 + 14040 = 17190.

Multiple choice

The wheels of bicycles A and B have radii 30 cm and 40 cm, respectively. While travelling a certain distance, each wheel of A required 5000 more revolutions than each wheel of B. If bicycle B travelled this distance in 45 minutes, then its speed, in km per hour, was

  1. 16 π

  2. 12 π

  3. 18 π

  4. 14 π
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let distance be D. Revolutions for A = D / (2 * pi * 30), for B = D / (2 * pi * 40). D/(60pi) - D/(80pi) = 5000. D/(240pi) = 5000, D = 1,200,000 * pi cm = 12 * pi km. Speed = Distance / Time = (12 * pi) / (45/60) = 12 * pi / 0.75 = 16 * pi km/hr.

Multiple choice

The distance from B to C is thrice that from A to B. Two trains travel from A to C via B. The speed of train 2 is double that of train 1 while traveling from A to B and their speeds are interchanged while traveling from B to C. The ratio of the time taken by train 1 to that taken by train 2 in travelling from A to C is

  1. 1 : 4

  2. 7 : 5

  3. 5 : 7

  4. 4 : 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance AB = d, then BC = 3d. Train 1 speed on AB = v, on BC = 2v. Train 2 speed on AB = 2v, on BC = v. Time for T1 = d/v + 3d/2v = 5d/2v. Time for T2 = d/2v + 3d/v = 7d/2v. Ratio T1:T2 = 5:7.

Multiple choice

Vimla starts for office every day at 9 am and reaches exactly on time if she drives at her usual speed of 40 km/hr. She is late by 6 minutes if she drives at 35 km/hr. One day, she covers two-thirds of her distance to office in one-thirds of her usual time to reach office, and then stops for 8 minutes. The speed, in km/hr, at which she should drive the remaining distance to reach office exactly on time is

  1. 29

  2. 27

  3. 28

  4. 26
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Usual time = D/40. Late by 6 min (0.1 hr) at 35 km/hr: D/35 - D/40 = 0.1. D/280 = 0.1, D = 28 km. Usual time = 28/40 = 0.7 hr (42 min). One day: 2/3 distance (18.66 km) in 1/3 time (14 min). Remaining distance = 9.33 km. Remaining time = 42 - 14 - 8 = 20 min (1/3 hr). Speed = 9.33 / (1/3) = 28 km/hr.

Multiple choice

Anil, Sunil and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and go in the clockwise direction. If they run at speeds of 15 km/hr, 10 km/hr and 8 km/hr, respectively, how much distance in km will Ravi have run when Anil and Sunil meet again for the first time at the starting point?

  1. 4.2

  2. 5.2

  3. 4.8

  4. 4.6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Time for Anil to complete a lap = 3/15 = 1/5 hr. Time for Sunil = 3/10 = 3/10 hr. They meet at the start when time is a multiple of both 1/5 and 3/10. LCM(1/5, 3/10) = 3/5 hr. In 3/5 hr, Ravi (speed 8 km/hr) runs 8 * 0.6 = 4.8 km.

Multiple choice

Two cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take 1.5 hours if they travel towards each other, but 10.5 hours if they travel in the same direction. If the speed of the slower car is 60 km/hr, then the distance traveled, in km, by the slower car when it meets the other car while traveling towards each other, is

  1. 150

  2. 100

  3. 90

  4. 120
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speeds be v1 and v2. (v1+v2) * 1.5 = D. (v1-v2) * 10.5 = D. 1.5(v1+v2) = 10.5(v1-v2). v1+v2 = 7(v1-v2). v1+v2 = 7v1-7v2. 8v2 = 6v1. v1 = 4/3 * v2. If v2=60, v1=80. D = (80+60)*1.5 = 140*1.5 = 210. Distance by slower car = 60 * 1.5 = 90.