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 bus starts at 9 am and follows a fixed route every day. One day, it traveled at a constant speed of 60 km per hour and reached its destination 3.5 hours later than its scheduled arrival time. Next day, it traveled two-thirds of its route in one-third of its total scheduled travel time, and the remaining part of the route at 40 km per hour to reach just on time. The scheduled arrival time of the bus is

  1. 10:30 pm

  2. 7:00 pm

  3. 7:30 pm

  4. 9:00 pm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let scheduled time be T. Distance D = 60 * (T + 3.5). Also, D = (2/3)D / (T/3) * (T/3) + (1/3)D / 40. This simplifies to a linear equation for T. Solving yields T = 10.5 hours. 9 am + 10.5 hours = 7:30 pm.

Multiple choice

Emma, a delivery driver for a local courier service, has a multi-stop route to complete. She drives her delivery van at an average speed of 40 kmph for 30% of the total distance while navigating city traffic, at 60 kmph for 40% of the total distance on highways, at 50 kmph for 20% of the total distance through suburban areas, and at 30 kmph for the remaining 10% of the total distance on rural roads. What is Emma's average speed for the entire journey?

  1. 42.61 kmph

  2. 46.51 kmph

  3. 54.15 kmph

  4. 61.54 kmph
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average speed = Total Distance / Total Time. Let total distance be D. Time = (0.3D/40) + (0.4D/60) + (0.2D/50) + (0.1D/30) = D * (0.0075 + 0.00666 + 0.004 + 0.00333) = D * 0.0215. Average speed = D / (0.0215D) = 46.51 kmph.

Multiple choice

Two cities, X and Y, are 60 km apart and connected by a straight highway. Rahul starts traveling from X to Y, while Priya starts from Y to X. They begin at the same time and cross each other exactly 2 hours after starting. If Rahul reaches Y exactly 1 hour 40 minutes after Priya reaches X, what is Rahul's speed in km per hour?

  1. 10 km/hr

  2. 12 km/hr

  3. 14 km/hr

  4. 16 km/hr

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

Let speeds be R and P. They meet in 2 hours, so 2(R+P) = 60, meaning R+P = 30. Rahul takes 60/R hours and Priya takes 60/P hours. Given 60/R = 60/P + 5/3, substituting P = 30-R leads to a quadratic equation. Solving for R gives 12 km/hr.

Multiple choice

A cyclist traveled a certain distance at a constant speed. If the speed had been increased by 4 km per hour, the journey would have taken 1 hour less. However, if the speed had been decreased by 5 km per hour, the journey would have taken 2 hours longer. What is the total distance, in km, covered by the cyclist?

  1. 120

  2. 180

  3. 200

  4. 220

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

Let d be distance and v be speed. d/v - d/(v+4) = 1 and d/(v-5) - d/v = 2. Solving these equations: d(v+4-v)/(v(v+4)) = 1 => 4d = v^2 + 4v. d(v-(v-5))/(v(v-5)) = 2 => 5d = 2v^2 - 10v. From first, d = (v^2+4v)/4. Substitute: 5(v^2+4v)/4 = 2v^2 - 10v => 5v^2 + 20v = 8v^2 - 40v => 3v^2 = 60v => v = 20. d = (400+80)/4 = 120.

Multiple choice

A car leaves City A at 7:30 AM and follows the same route every day. On one particular day, it travels at a steady speed of 48 km/h and arrives at its destination 2 hours later than its usual scheduled arrival time. The following day, the car covers three-fourths of the distance in half of the scheduled travel time, and covers the remaining distance at 32 km/h, reaching exactly on time. What is the car's usual scheduled arrival time?

  1. 5 : 30 PM

  2. 2 : 30 PM

  3. 1 : 30 PM

  4. 3 : 00 PM
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let D be distance and T be scheduled time. D/48 = T + 2. Also, (3/4)D / (T/2) + (1/4)D / 32 = T. Solving these equations: D = 48(T+2). Substitute: 1.5D/T + D/128 = T. 72(T+2)/T + 48(T+2)/128 = T. Solving for T gives T = 6 hours. 7:30 AM + 6 hours = 1:30 PM.

Multiple choice

Two cyclists, P and Q, start from two towns, M and N, and ride towards each other on a straight path at the same time. After meeting at a point along the way, P takes 5 hours more than Q to reach his destination. If P was cycling at a speed that is 3 km/hr less than the speed of Q, then which of the following can be the speed of Q and the time taken (in hours) to meet, respectively?

  1. 8 km/hr and 7 hours

  2. 9 km/hr and 6 hours

  3. 10 km/hr and 5 hours

  4. 12 km/hr and 4 hours
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let v be the speed of Q, so P's speed is v-3. Let t be the time to meet. Distance M to meeting point is (v-3)t, and N to meeting point is vt. After meeting, P covers the distance vt at speed v-3, taking vt/(v-3) hours. Q covers (v-3)t at speed v, taking (v-3)t/v hours. The difference is 5 hours. Testing option B: v=9, v-3=6. Meeting time t=6. P takes (9*6)/6 = 9 hours. Q takes (6*6)/9 = 4 hours. 9-4=5, which matches.

Multiple choice

A robotic vehicle was assigned to cover a fixed distance on a test track at a constant speed. If its speed had been increased by 3 km/hr, it would have completed the journey 3 hours sooner. On the other hand, if its speed had been reduced by 2 km/hr, it would have taken 7 hours longer. What was the distance, in kilometers, that the robot travelled?

  1. 32

  2. 24

  3. 28

  4. 18
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance be D and speed be v. D/v - D/(v+3) = 3 and D/(v-2) - D/v = 7. Solving these equations: D = 3v(v+3)/3 = v(v+3) and D = 7v(v-2)/2. Equating them: 2v(v+3) = 7v(v-2) -> 2v+6 = 7v-14 -> 5v = 20 -> v = 4. D = 4(4+3) = 28.

Multiple choice

A drone was used to deliver parcels across a city. It flew a certain distance at a constant speed. If its speed had been 6 km/h faster, it would have taken 2 hours less. If its speed had been 8 km/h slower, it would have taken 8 hours more. What was the distance, in km, that the drone travelled?

  1. 316

  2. 288

  3. 264

  4. 105

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

Let v be the speed and t be the time. From the given conditions, we set up the equations (v + 6)(t - 2) = vt and (v - 8)(t + 8) = vt, which simplify to v - 3t = -6 and v - t = 8. Solving this system gives t = 7 hours and v = 15 km/h, resulting in a total distance of 15 * 7 = 105 km.

Multiple choice

A cargo vessel sailed a fixed distance over the ocean at a constant speed. If its speed had been 9 km/h faster, it would have taken 2 hours less to complete the journey. If its speed had been 9 km/h slower, the journey would have taken 4 hours more. What was the original speed, in km/h, of the vessel?

  1. 18

  2. 27

  3. 36

  4. 44

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

Let the original speed and time be v and t. The distance equations are (v + 9)(t - 2) = vt and (v - 9)(t + 4) = vt. These give 9t = 2v + 18 and 9t = 4v - 36, so v = 27 km/h.

Multiple choice

Two cars started from the same point and travelled on a straight course in opposite directions for exactly 2 hours. At that time they were 208 miles apart. If one car, is faster than the other car by an average of 8 miles per hour, what was the average speed (in miles/hr) of the slower car for the two hour trip?

  1. 32 miles per hour

  2. 40 miles per hour

  3. 48 miles per hour

  4. 56 miles per hour

  5. 60 miles per hour
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the speed of the slower car be x. The faster car's speed is x+8. In 2 hours, the total distance covered by both is 2(x) + 2(x+8) = 208. Solving 4x + 16 = 208 gives 4x = 192, so x = 48.

Multiple choice

A person walking at the speed of 3 km/hr was overtaken by a carriage. It being a foggy day, the sight distance was limited to 100 metres. The person was able to see the carriage for 30 seconds only. Find the speed of the carriage.

  1. 21 km/hr

  2. 19 km/hr

  3. 16 km/hr

  4. 15 km/hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The relative speed of the carriage with respect to the person is distance / time = 100 m / 30 s = 10/3 m/s. Converting to km/hr: (10/3) * (18/5) = 12 km/hr. Since the carriage overtakes the person, the carriage speed = person speed + relative speed = 3 + 12 = 15 km/hr.