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

An object travel $10\ km$ at a speed of $100\ m/s$ and another $10\ km$ at $50\ m/s$. The average speed over the whole distance is
  1. $75\ m/s$
  2. $55\ m/s$
  3. $66.7\ m/s$
  4. $33.3\ m/s$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average speed = Total distance / Total time. Distance 1 = 10 km = 10000 m. Time 1 = 10000 / 100 = 100 s. Distance 2 = 10000 m. Time 2 = 10000 / 50 = 200 s. Total distance = 20000 m. Total time = 300 s. Average speed = 20000 / 300 = 66.7 m/s.

Multiple choice

A boy walks to his school at a distance of $6\;km$ with a speed of $2.5\;km/h$ and walks back with a constant speed by $4 \;km/h$. His average speed for trip expressed in $km/h$ is
  1. $\displaystyle \frac{24}{13}$
  2. $\displaystyle \frac{40}{13}$
  3. $3$
  4. $4.8$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average speed = Total distance / Total time. Total distance = 6 + 6 = 12 km. Time 1 = 6 / 2.5 = 2.4 hours. Time 2 = 6 / 4 = 1.5 hours. Total time = 3.9 hours. Average speed = 12 / 3.9 = 120 / 39 = 40 / 13 km/h.

Multiple choice

A particle starts from east and travels a distance $S$ with uniform acceleration, then it travels a distance $2S$ with uniform speed, finally it travels a distance $3S$ with uniform retardation and comes to rest. If the complete motion of the particle is a straight line then the ratio of its average to maximum velocity is:
  1. $\displaystyle \dfrac{6}{7}$
  2. $\displaystyle \dfrac{4}{5}$
  3. $\displaystyle \dfrac{3}{5}$
  4. $\displaystyle \dfrac{2}{5}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The motion consists of three phases: acceleration, constant speed, and retardation. By calculating the time taken for each phase in terms of maximum velocity v, the total distance and total time are found to be 6S and 10S/v respectively. The average velocity is total distance divided by total time, which simplifies to 0.6v, or 3/5 of the maximum velocity.

Multiple choice

A man travels $600$ km by train at $800$ km / hr, $800$ km by ship at $40$ km/hr, $500$ km by aeroplane at $400$ km/hr and $100$ km by car at $50$ km/hr. What is the average speed for the entire distance ?
  1. $60$ km/hr
  2. $\displaystyle 60\frac{5}{123}$ km/hr
  3. $62$ km/hr
  4. $\displaystyle 83\frac{1}{3}$ km/hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total distance = 600 + 800 + 500 + 100 = 2000 km. Total time = 600/800 + 800/40 + 500/400 + 100/50 = 0.75 + 20 + 1.25 + 2 = 24 hours. Average speed = 2000 / 24 = 83.33 km/hr.

Multiple choice

A particle travels half of total distance with speed $v_1$ and next half with speed $v_2$ along a straight line. Find out the average speed of the particle?
  1. $\displaystyle \frac{2v_1v_2}{v_1\, +\, v_2}$
  2. $\displaystyle \frac{2v_1v_2}{v_1\, -\, v_2}$
  3. $\displaystyle \frac{v_1\, +\, v_2}{2v_1v_2}$
  4. $\displaystyle \frac{v_1\, -\, v_2}{2v_1v_2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Average speed is total distance divided by total time. Let total distance be 2d. Time taken for first half = d/v1. Time taken for second half = d/v2. Total time = d/v1 + d/v2 = d(v1+v2)/(v1*v2). Average speed = 2d / [d(v1+v2)/(v1*v2)] = 2*v1*v2 / (v1+v2).

Multiple choice

Armaan goes 10 km distance with average speed of 6 km/hr while the rest 20 km he travels with an average speed of 15 km/hr. What is the average speed of Armaan during the whole journey?

  1. 10 km/hr

  2. 12 km/hr

  3. 13 km/hr

  4. 14.5 km/hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Average speed = Total distance / Total time. Total distance = 10 + 20 = 30 km. Time 1 = 10/6 = 5/3 hours. Time 2 = 20/15 = 4/3 hours. Total time = 5/3 + 4/3 = 9/3 = 3 hours. Average speed = 30 / 3 = 10 km/hr.

Multiple choice

A bus travels the first one third distance at a speed of $\displaystyle 10 km\ { h }^{ -1 }$, the next one third distance at a speed of $\displaystyle 20 km\ { h }^{ -1 }$ and the next one third distance at a speed of $\displaystyle 30 km\ { h }^{ -1 }$ .
  1. $\displaystyle 20 \quad { ms }^{ -1 }$
  2. $\displaystyle \frac { 50 }{ 11 } { ms }^{ -1 }$
  3. $\displaystyle \frac { 180 }{ 11 } { ms }^{ -1 }$
  4. $\displaystyle 30 \quad { ms }^{ -1 }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For equal distances, the average speed is the harmonic mean: 3 divided by (1/10 + 1/20 + 1/30), which equals 180/11 km/hr. Converting to m/s gives (180/11) × 5/18 = 50/11 m/s.

Multiple choice

A person travels two parts of the total distance in the ratio 2 : 1 with constant speed of $\displaystyle { 30 km }\ { h }^{ -1 }\ and \ { 40 km }\ { h }^{ -1 }$ respectively. The average speed of the journey is ____ $\displaystyle { km } { h }^{ -1 }$
  1. $13.5$ 
  2. $62.2$ 
  3. $42.5$ 
  4. $32.7$ 
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Average speed = Total Distance / Total Time. Let total distance be 3D. Part 1 = 2D, time = 2D/30. Part 2 = D, time = D/40. Total time = 2D/30 + D/40 = 8D/120 + 3D/120 = 11D/120. Average speed = 3D / (11D/120) = 360/11 = 32.72.

Multiple choice

A lizard, at an initial distance of $21$ cm behind an insect, moves from rest with an acceleration of $2 cm/s^{2}$ and pursues the insect which is crawling uniformly along a straight line at a speed of $20$ cm/s. Then the lizard will catch the insect after
  1. $20$ s
  2. $1$ s
  3. $21$ s
  4. $24$ s
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let t be time. Distance covered by lizard = 0.5 * a * t^2 = 0.5 * 2 * t^2 = t^2. Distance covered by insect = 20t. The lizard catches the insect when t^2 = 21 + 20t. Solving t^2 - 20t - 21 = 0 gives (t - 21)(t + 1) = 0. Since t > 0, t = 21 seconds.

Multiple choice

The average speed of a car is $\dfrac {9}{5}$ times the average speed of a bus. A tractor covers $575$ km in $23$ hours. How much distance will the car cover in $4$ hours, if the speed of the bus is twice the speed of the tractor?
  1. $340$ km
  2. $360$ km
  3. $450$ km
  4. $480$ km

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

Tractor speed = 575 / 23 = 25 km/h. Bus speed = 2 * 25 = 50 km/h. Car speed = (9/5) * 50 = 90 km/h. Distance = 90 * 4 = 360 km.