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 car starts from rest and accelerates uniformly at the rate of $ 10 cms^{-2} $ and reaches a maximum velocity of $72 kmph$. it travels with this maximum velocity for some time and retards uniformly at the rate of $ 20 cms^{-2} $ and comes to a stop. if the total distance covered by the body is $ 5 km$, find the total time of travel of the body in sec
  1. $200$
  2. $250$
  3. $300$
  4. $400$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Convert units: 72 km/h = 20 m/s. Acceleration = 0.1 m/s^2, Retardation = 0.2 m/s^2. Time to reach max velocity: t1 = 20 / 0.1 = 200 s. Distance during acceleration: d1 = 0.5 * 0.1 * 200^2 = 2000 m. Time to stop: t3 = 20 / 0.2 = 100 s. Distance during retardation: d3 = 0.5 * 0.2 * 100^2 = 1000 m. Remaining distance = 5000 - 2000 - 1000 = 2000 m. Time at constant velocity: t2 = 2000 / 20 = 100 s. Total time = 200 + 100 + 100 = 400 s.

Multiple choice

When two bodies approach each other with the different speeds, the distance between them decreases by $120$$\mathrm { m }$ for every $1 \mathrm { min }$ . The speeds of the bodies are
  1. $2 \mathrm { m } / \mathrm { s }$ and $0.5 \mathrm { m } / \mathrm { s }$
  2. $3 \mathrm { m } / \mathrm { s }$ and $2 \mathrm { m } / \mathrm { s }$
  3. $1.75 \mathrm { m } / \mathrm { s }$ and $0.25 \mathrm { m } / \mathrm { s }$
  4. $2.5 \mathrm { m } / \mathrm { s }$ and $0.5 \mathrm { m } / \mathrm { s }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Two cars $A$ and $B$ are moving with same speed of 45$\mathrm { km } / \mathrm { hr }$ along same direction. If a third car C coming from opposite direction with a speed of 36$\mathrm { km }$ hr meets two cars in an interval of 5 minutes, the distance of separation of two cars $A$ and B should be $( i n k m )$

  1. 6.75

  2. 7.25

  3. 5.55

  4. 8.35
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Relative speed of C with respect to A and B = 45 + 36 = 81 km/hr. Time interval = 5 min = 5/60 hr = 1/12 hr. Distance = speed * time = 81 * (1/12) = 6.75 km.

Multiple choice

A bus moving with a speed of $10m/s$ on a straight road. A scooterist wishes to overtake the bus in $100s$. If the bus is at a distance of $1km$ from the scooterist, with what speed should the scooterist chase the bus?
  1. $10m/s$
  2. $20 m/s$
  3. $40 m/s$
  4. $25 m/s$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Relative speed = Distance / Time. The distance is 1000m and time is 100s, so relative speed = 10m/s. Since the bus is moving at 10m/s, the scooterist must travel at 10m/s + 10m/s = 20m/s.

Multiple choice

A car travels the first one-third distance at a speed of $10\ km/hr$, the next one-third distance at $20\ km/hr$ and the last one-third distance at $60\ km/hr$. The average speed of the car is
  1. $14\ km/hr$
  2. $16\ km/hr$
  3. $18\ km/hr$
  4. $20\ km/hr$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average speed = Total distance / Total time. Let total distance be 3d. Time taken = d/10 + d/20 + d/60 = (6d+3d+d)/60 = 10d/60 = d/6. Average speed = 3d / (d/6) = 18 km/hr.

Multiple choice

The total distance between two stations is $570$ km out of which , $224$ km is covered at $56$ km/hr, $210$ km is covered at $70$ km/hr and remaining is covered in $2$ hours. Find the average speed during the whole journey.
  1. $ 14\cfrac{1}{3} $ km/hr
  2. $ 52\cfrac{1}{3} $ km/hr
  3. $ 75\cfrac{1}{3} $ km/hr
  4. $ 63\cfrac{1}{3} $ km/hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total distance = 570 km. Part 1: 224 km at 56 km/hr = 4 hours. Part 2: 210 km at 70 km/hr = 3 hours. Remaining distance = 570 - 224 - 210 = 136 km. Time for remaining = 2 hours. Total time = 4 + 3 + 2 = 9 hours. Average speed = 570 / 9 = 63.33 km/hr = 63 1/3 km/hr.

Multiple choice

Out of a total distance of $200$ km covered, first half is covered at the speed of $60$ km/hr and the remaining half is covered at $75$ km/hr . Find the average speed for the whole journey.
  1. $ 21\dfrac{2}{3}$ km/hr
  2. $ 66\dfrac{2}{3}$ km/hr
  3. $ 43\dfrac{2}{3}$km/hr
  4. $ 39\dfrac{2}{3}$ km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average speed is total distance divided by total time. Total distance is 200 km. Time for first 100 km is 100/60 = 5/3 hours. Time for second 100 km is 100/75 = 4/3 hours. Total time is 5/3 + 4/3 = 3 hours. Average speed = 200/3 = 66 2/3 km/hr.