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 motor boat named "Destiny" goes downstream from point A to point B and returns immediately. The distance from A to B is equal to the distance travelled by a person at 6 km/hr in 20 hours. It takes the boat 15 hours to complete the whole trip. If the speed of the river were twice, then "Destiny" would took 24 hours to complete the downstream and upstream trip. Which of the following can be obtained from the above given information? (i) Speed of the stream (ii) Speed of "Destiny" in still water (iii) Distance covered by "Destiny" in still water in 10 hours (iv) Time taken by "Destiny" to cover the distance of 216 km in still water

  1. Only (i)

  2. Only (i) and (ii)

  3. Only (iii) and (ii)

  4. All (i), (ii), (iii) and (iv)

  5. Only (i), (ii) and (iv)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The distance AB is 6 * 20 = 120 km. Let boat speed be u, stream speed v. 120/(u+v) + 120/(u-v) = 15. With 2v: 120/(u+2v) + 120/(u-2v) = 24. These equations allow solving for u and v, and subsequently answering all parts.

Multiple choice

Directions: In the question, two quantities are given, one as 'Quantity 1' and another as 'Quantity 2'. You have to determine relationship between the two quantities and choose the appropriate option. A girl travelled 15 km. She travelled the first 1/5 part of the total distance at the speed of 1.5 km/hr, the next 1/3 part of the total distance at the speed of 2.5 km/hr and the remaining distance at the speed of X km/hr in 2.8 hrs. Quantity 1: The value of X. Quantity 2: 2.1

  1. Quantity 1 > Quantity 2

  2. Quantity 1 ≥ Quantity 2

  3. Quantity 2 > Quantity 1

  4. Quantity 2 ≥ Quantity 1

  5. Quantity 1 = Quantity 2 or relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

A man can row a distance of y km upstream in 4 hours. Find his speed in still water. (I) The speed of current is 1.5 km/hr. (II) He covers a distance of 60 km downstream in 5 hours. (III) He covers the distance of y km downstream in 3 hours.

  1. Only I & II

  2. Only I & III

  3. All I, II & III

  4. Any two of them

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

Let still water speed = x, current speed = c. Upstream: (x-c)×4 = y. We need x. Statement I: c=1.5, but y unknown. Statement II: (x+c)×5=60, but c unknown. Statement III: (x+c)×3=y, relates y and x+c. No single pair suffices - you need all three to solve. Any two statements leave too many unknowns.

Multiple choice

A man can walk uphill at the rate of 2.5 km/hr. and downhill at the rate of 3.25 km/hr. If the total time required to walk a certain distance up the hill and return to the starting position in 4h. 36 min. What is the distance he walked up the hill?

  1. 3.5 km.

  2. 4.5 km.

  3. 5.5 km.

  4. 6.5 km.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let distance up the hill be d km. Time up = d/2.5 hours, time down = d/3.25 hours. Total time = d/2.5 + d/3.25 = 4 hours 36 minutes = 4.6 hours. Multiplying by 325: 130d + 100d = 1494.5, so 230d = 1494.5, giving d = 6.5 km. Verification: 6.5/2.5 = 2.6 hr up, 6.5/3.25 = 2 hr down, total = 4.6 hr = 4hr 36min.

Multiple choice

A cycled from P to Q at 10 km/hr and returned at the rate of 9 km/hr. B cycled bothways at 12 km/hr. It was discovered that for the total journey B took ten minutes less than A. What is the distance between P and Q?

  1. 2.75 km.

  2. 3.75 km.

  3. 7.5 km.

  4. 9 km.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let distance = d km. A's time = d/10 + d/9 = (9d+10d)/90 = 19d/90 hours. B's time = 2d/12 = d/6 hours. B took 10 minutes less: d/6 - 19d/90 = 10/60. Converting: (15d-19d)/90 = 1/6, so -4d/90 = 1/6. This gives d = -90/24 = -3.75, but taking absolute value and reconsidering the equation setup: Actually A took MORE time, so 19d/90 - d/6 = 1/6, giving 4d/90 = 15/90, so d = 15/4 = 3.75 km.

Multiple choice

A father and his son start a point P with speed of 16 km/hr. and 24 km/hr. respectively and reach another point Q. If his son starts 60 min after his father at P and reaches Q 60 min. before his father, what is the distance between P and Q?

  1. 86 km.

  2. 72 km.

  3. 94 km.

  4. 96 km.

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

Father's time = d/16 hours. Son starts 60 min (1 hour) later, so son's travel time = d/24 hours. Son reaches 60 min (1 hour) before father. So: d/16 = d/24 + 1 + 1 = d/24 + 2. Multiply by 48: 3d = 2d + 96, so d = 96 km. Option D is correct.

Multiple choice

A certain distance is covered by a cyclist at a certain speed. If a jogger covers half the distance in double the time, the ratio of the speed of the jogger to that of the cyclist is -

  1. 1 : 4

  2. 4 : 1

  3. 1 : 2

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

Let the cyclist's speed be v and time be t, so distance d = vt. The jogger covers d/2 distance in 2t time, so jogger's speed = (d/2)/(2t) = d/4t = v/4. Therefore, jogger's speed : cyclist's speed = v/4 : v = 1 : 4.

Multiple choice

The distance between places A and B is 999 km. An express train leaves place A at 6 am and runs at a speed of 55.5 km/hr. The train stops on the way for 1 hr. 20 min. It reaches B at-

  1. 1:20 am

  2. 12 pm

  3. 6 pm

  4. 11 pm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total time needed = distance/speed = 999/55.5 = 18 hours. With a stop of 1 hour 20 minutes, total journey time = 18 hours + 1 hour 20 minutes = 19 hours 20 minutes. Starting from 6 am, adding 19 hours 20 minutes gives 1:20 am the next day.

Multiple choice

Raj can row a certain distance downstream in 12 hours and can return the same distance in 18 hours. If the stream flows at the rate of 6 km/hr, find the speed of Raj in still water.

  1. 15 km/hr

  2. 20 km/hr

  3. 25 km/hr

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

Let downstream speed = (d+6) km/hr and upstream speed = (d-6) km/hr where d is speed in still water. Distance is same: 12(d+6) = 18(d-6). Solving: 12d+72 = 18d-108, so 6d = 180 and d = 30 km/hr. The distance cancels out when equating both expressions.

Multiple choice

John started from A to B and Vinod from B to A. If the distance between A and B is 125 km. and they meet at 75 km. from A, what is the ratio of John's speed to that of Vinod's speed?

  1. 3:2

  2. 5:3

  3. 4:5

  4. 3:5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When two people start from opposite ends and meet, the ratio of their speeds equals the ratio of distances covered. John covers 75 km and Vinod covers 125-75 = 50 km when they meet. Therefore, the ratio of John's speed to Vinod's speed = 75:50 = 3:2. This is because they travel for the same duration until meeting, so speed ratio directly equals distance ratio.

Multiple choice

A person swims a distance of 28 km. in the direction of stream in 5 hours and a distance of 13 km. in 5 hours against the stream. What is the speed of the stream?

  1. 2 km./hr.

  2. 1.5 km./hr.

  3. 2.5 km./hr.

  4. 1.8 km./hr.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Downstream speed = 28/5 = 5.6 km/h. Upstream speed = 13/5 = 2.6 km/h. Stream speed = (downstream - upstream)/2 = (5.6 - 2.6)/2 = 3/2 = 1.5 km/h. This is a standard formula: speed of current = (speed with stream - speed against stream) / 2.

Multiple choice

With an average speed of 40 km/hr. a train reaches its destination on time.If it goes with an average speed of 35 km./hr. it is late by 15 minutes.The total journey is -

  1. 80 km.

  2. 40 km.

  3. 70 km.

  4. 30 km.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance = d km. At 40 km/h: time = d/40 hours. At 35 km/h: time = d/35 hours. Difference = 15 min = 0.25 hours. So d/35 - d/40 = 0.25. Solving: d(1/35 - 1/40) = 0.25 → d(5/1400) = 0.25 → d = 0.25 × 280 = 70 km. At 70 km, time at 40 km/h = 1.75 hr; at 35 km/h = 2 hr (15 min late).