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

Alice and Bob decide to run a race. Alice runs the first half of the race at an average speed of 15 miles per hour and the second half at 20 miles per hour. On the other hand, Bob covers the same distance and with same speeds of 15 miles per hour and 20 miles per hour, with the ratio of the distances covered at these speeds being 3 : 4.Quantity AAlice's average speed for the entire distanceQuantity BBob's average speed for the entire distance

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Alice's average speed = 2 * v1 * v2 / (v1 + v2) = 2 * 15 * 20 / (15 + 20) = 600 / 35 = 17.14 mph. Bob's average speed = Total Distance / Total Time. Let distance be 7d. Bob covers 3d at 15 mph and 4d at 20 mph. Time = 3d/15 + 4d/20 = d/5 + d/5 = 2d/5. Average speed = 7d / (2d/5) = 35/2 = 17.5 mph. Bob's speed is greater.

Multiple choice

Raj and Vishal are two friends who complete their travel journey from point A to B by using four different modes of transport: bicycle, bus, scooter, and car, which move at the speeds of 10, 20, 30, and 40 kmph, respectively. To travel from point A to B, Raj uses each mode of transport for 1 4 t h of his total journey time, while Vishal takes each mode of transport for 1 4 t h of the total distance. The approximate percentage by which Vishal's travel time exceeds Raj's travel time is:

  1. 15

  2. 30

  3. 45

  4. 60

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

Raj's average speed is the arithmetic mean because he spends equal time at each speed, giving 25 km/h. Vishal's average speed is the harmonic mean because he covers equal distances, giving about 19.2 km/h, so his travel time is about 30% greater.

Multiple choice

A car travels a distance of 180 kilometers in 3 hours, while a motorcycle covers the same distance in 4 hours. Quantity A Average speed of the motorcycle in kilometers per hour Quantity B Average speed of the car in kilometers per hour

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Speed of car = 180 / 3 = 60 km/hr. Speed of motorcycle = 180 / 4 = 45 km/hr. Quantity B (60) is greater than Quantity A (45).

Multiple choice

A and B are two stations 455 km apart. A train starts from station A at 9 am and runs towards station B with a speed of 55 kmph. Another train starts from station B at 10 am and runs towards station A with a speed of 45 kmph. At what time do the trains meet? 1.2 pm 2. 2:15 pm 3.2:30 pm 4.2:45 pm

  1. 1

  2. 2

  3. 3

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

Train A starts at 9 am, speed 55. By 10 am, it has traveled 55 km. Remaining distance = 455 - 55 = 400 km. Relative speed = 55 + 45 = 100 kmph. Time to meet = 400 / 100 = 4 hours after 10 am, which is 2 pm.

Multiple choice

Ratio of the time taken by the boat travel 150 km against stream to time taken to covers the same distance along with stream is 5: 1. If the speed of the stream is 20 kmph, then what is the speed of boat in still water?

  1. 40 kmph

  2. 25 kmph

  3. 30 kmph

  4. 45 kmph

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

Let v be the boat speed and s=20 be the stream speed. The time ratio (distance/(v-s)) / (distance/(v+s)) = 5/1 simplifies to (v+s)/(v-s) = 5/1. Solving v+20 = 5(v-20) gives v+20 = 5v-100, so 4v = 120 and v = 30 kmph.

Multiple choice

On a straight highway, points C and D are located such that point D is 360 km East of point C. Car P starts from point C, and car Q starts from point D at the same time. If they both move towards each other, they meet after 2 hours. If they both move in the same direction, they meet in 6 hours. What are their speeds?

  1. 120 kmph and 60 kmph

  2. 126 kmph and 54 kmph

  3. 130 kmph and 50 kmph

  4. 100 kmph and 50 kmph
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let speeds be u and v. When moving towards each other, relative speed is u + v = 360/2 = 180. When moving in the same direction, relative speed is |u - v| = 360/6 = 60. Solving u + v = 180 and u - v = 60 gives u = 120 and v = 60.

Multiple choice

A man travels from Point P to Q with 90 km/hr and from Q to R with 60 km/hr. Total distance between P to R is 200 km. If his average speed is 75 km/hr then find the distance between P and Q?

  1. 76

  2. 79

  3. 120

  4. 34

  5. 52
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let d be the distance from P to Q, so 200-d is the distance from Q to R. The total time is d/90 + (200-d)/60 = 200/75. Solving this equation, d/90 + (200-d)/60 = 8/3 leads to 2d + 3(200-d) = 480, which simplifies to 600-d = 480, so d = 120.

Multiple choice

DIRECTION for the question: Solve the following question and mark the best possible option. A motorist covers a distance of 39 km in 45 minutes by moving at a speed of x kmph for the first 15 minutes, then moving at a double the speed for the next 20 minutes and then again moving at his original speed for the rest of the journey. Then, x is equal to :

  1. 36

  2. 22

  3. 25

  4. 340

  5. 30
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total distance = 39 km. Time = 45 min = 0.75 hours. Let speed be x. 15 min = 0.25 h, 20 min = 1/3 h, 10 min = 1/6 h. Distance = (x * 0.25) + (2x * 1/3) + (x * 1/6) = 39. (1/4 + 2/3 + 1/6)x = 39. (3/12 + 8/12 + 2/12)x = 39. (13/12)x = 39. x = 39 * 12 / 13 = 3 * 12 = 36 kmph.

Multiple choice

A boat goes 36 km downstream in 3 hours and returns the same distance upstream in 6 hours. If the speed of the stream increases by 2 km/h, how much time will it take to return upstream over the same distance?

  1. 9 hours

  2. 7 hours

  3. 8 hours

  4. 10 hours

  5. 12 hours
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Downstream speed = 36/3 = 12 km/h. Upstream speed = 36/6 = 6 km/h. Stream speed = (12-6)/2 = 3 km/h. Boat speed = 9 km/h. New stream speed = 3+2 = 5 km/h. New upstream speed = 9-5 = 4 km/h. Time = 36/4 = 9 hours.

Multiple choice

The time taken by car A to cover 3x km is equal to the time taken by car B to cover 2x km and the speed of car A is 15 km/hr more than that of B. If the speed of car B is increased by 4 km/hr, then find the time taken by car B to cover 170km.

  1. 2 hours

  2. 8 hours

  3. 4 hours

  4. 5 hours

  5. 11 hours
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Time A = 3x/Va, Time B = 2x/Vb. 3x/Va = 2x/Vb => Va = 1.5Vb. Also Va = Vb + 15. 1.5Vb = Vb + 15 => 0.5Vb = 15 => Vb = 30. New speed of B = 30 + 4 = 34. Time = 170 / 34 = 5 hours.