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

During one month, Aisha swam s miles at a speed of 3 miles per hour and hiked h miles at a speed of 6 miles per hour. She swam and hiked a total of 90 miles that month, and she spent twice as much time hiking as she did swimming. What is the total number of miles Aisha hiked during the month?

  1. 30

  2. 45

  3. 60

  4. 72
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Ts be time swimming, Th be time hiking. Ts = s/3, Th = h/6. Total distance s+h = 90. Th = 2 * Ts => h/6 = 2 * (s/3) => h/6 = 2s/3 => h = 4s. Substitute into s+h=90: s+4s=90 => 5s=90 => s=18. Then h=72.

Multiple choice

Anisha completed the distance of 96km two hours earlier than she planned to do it. This was achieved by travelling 1 km more every hour than she intended to cover every 1 hr 15 mins. What was the speed to which Anisha travelled during the whole ?

  1. 26 km/hr

  2. 16 km/hr

  3. 36 km/hr

  4. 30 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let original speed be v and time be t. 96/v = t. New speed is v+1, new time is t-2. The distance is 96. Solving the system leads to v=16 km/hr.

Multiple choice

s = 60t The equation above can be used to calculate the distance s, in miles, traveled by a bus moving at a speed of 60 miles per hour over a period of t hours. For any positive constant k, the distance the bus would have traveled after 10k hours is how many times the distance the bus would have traveled after 2k hours?

  1. 4

  2. 5

  3. 5k

  4. 7k
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Distance s = 60t. Distance at 10k hours is 60 * 10k = 600k. Distance at 2k hours is 60 * 2k = 120k. The ratio is 600k / 120k = 5.

Multiple choice

A thief saw a policeman, and he started running at a speed of 18 m/s. After 12 seconds, the policeman starts running behind the thief at a certain speed. If the policeman covered 864 meters distance to reach the thief, then the speed (in m/s) of the policeman is:

  1. 15

  2. 30

  3. 24

  4. 28
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Thief runs for 12s at 18m/s, distance = 216m. Policeman covers 864m. Time taken by policeman = t. Time taken by thief = t + 12. Distance of thief = 18 * (t + 12) = 216 + 18t. Total distance of thief = 216 + 18t = 864. 18t = 648, t = 36s. Speed of policeman = 864 / 36 = 24 m/s.

Multiple choice

A policeman saw a thief at a distance of 400 metres away. The thief started running at a speed of 10 km/h and the policeman chased him at a speed of 12 km/h in the same direction. At what distance from the starting point will the policeman catch the thief?

  1. 2.4 km

  2. 3 km

  3. 2 km

  4. 2.8 km
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Relative speed = 12 - 10 = 2 km/h. Time to catch = Distance / Relative speed = 0.4 km / 2 km/h = 0.2 hours. Distance covered by policeman = 12 km/h * 0.2 h = 2.4 km.

Multiple choice

A boat P travels 40 km upstream from point A to B in 10 hours and from point B to A downstream in 5 hours. Another boat Q can travel from point A to a point C, 30 km upstream, in 5 hours. At 10 am, P starts from A and goes towards B. At the same time, Q starts from C and proceeds towards A. What is the speed of the boat Q in still water?

  1. 6 kmph

  2. 8 kmph

  3. 10 kmph

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

Boat P's upstream speed is 4 kmph (40/10) and downstream speed is 8 kmph (40/5). The speed of boat P in still water is (8+4)/2 = 6 kmph, and the stream speed is (8-4)/2 = 2 kmph. Boat Q travels 30 km upstream in 5 hours, so its upstream speed is 6 kmph. Since Q's speed in still water minus the stream speed (2 kmph) equals 6 kmph, Q's speed in still water is 8 kmph.

Multiple choice

Ranvir goes to his office from his house at a speed of 16 km/hr and returns to his home from his office at a speed of 20 km/hr and he takes 4 hour 30 minutes in all. If the distance of his friend's house from his office is 20% more than the distance of his house from his office, find the distance of his house to his friend's house.(assuming the office lies between Ranvir's house and his friend's house)

  1. 80 km

  2. 60 km

  3. 92 km

  4. 88 km
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let d be the distance from house to office. Time = d/16 + d/20 = 4.5 hours. (5d + 4d)/80 = 4.5 => 9d/80 = 4.5 => d = 4.5 * 80 / 9 = 40 km. Distance from house to friend's house = d + 1.2d = 2.2d = 2.2 * 40 = 88 km.

Multiple choice

A man can row at a speed of 15/2 km/hr in still water. If he takes 4 times as long to row a distance upstream as to row the same distance downstream, then the speed of stream (in km/hr) is

  1. 4

  2. 3.75

  3. 5

  4. 4.5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let v be the speed of the stream. Downstream speed is 7.5 + v, and upstream speed is 7.5 - v. Since time = distance / speed and time_up = 4 * time_down, we have 1 / (7.5 - v) = 4 / (7.5 + v). Solving this gives 7.5 + v = 30 - 4v, so 5v = 22.5, which means v = 4.5.

Multiple choice

A swimmer swims from a point A against a current for 10 minutes before he reaches point C and then swims back along the current for next 10 minutes and comes to point B. If the distance between A and B is 200 metres, find the speed of the current (in kmph) :

  1. 0.6

  2. 0.5

  3. 0.4

  4. 0.9
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let v be swimmer speed and c be current speed. Distance A to C = (v-c) * (10/60). Distance C to B = (v+c) * (10/60). A to B = AC - CB = (v-c)/6 - (v+c)/6 = -2c/6 = -c/3. The magnitude is 200m = 0.2km. So c/3 = 0.2, c = 0.6 kmph.

Multiple choice

A, B and C are situated at the bank of river which is flowing at a constant rate. B is at an equal distance with A and C. A swimmer Avinash takes 10 h to swim from A to B and B to A. Also, he takes 4 h to swim from A to C. What is the ratio of speed of Avinash is still water and speed of stream?

  1. 5 : 3

  2. 3 : 5

  3. 2 : 5

  4. 1 : 2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let speed of boat be u and stream be v. Distance AB = d. Time AB + BA = d/(u+v) + d/(u-v) = 10. Time AC = d/(u-v) = 4. Solving these gives u/v = 5/3.

Multiple choice

At his usual rowing speed, kapil can travel 12 miles downstream in a certain riven in 6 h less than he takes to travel the same distance upstream. But, if he could double his usual rowing speed for his 24 mile round trip, the downstream 12 miles would then take only 1 h less than the upstream 12 miles, what is the speed of the current in mile/h?

  1. 2 2/3 mile/h

  2. 3 2/3 mile/h

  3. 5 2/3 mile/h

  4. 7 2/3 mile/h
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let v be rowing speed and c be current speed. The equations derived from the two scenarios (12/(v-c) - 12/(v+c) = 6 and 12/(2v-c) - 12/(2v+c) = 1) allow solving for c. Solving these yields c = 8/3 or 2 2/3 mph.