Quantitative Aptitude

Time, Speed and Distance

2,165 Questions
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Time, Speed and Distance Questions

Multiple choice

A bus takes $5$ hours more than a train to cover the distance of $900\ km$ from Vardha to Pune. If speed of the train is $15\ km/hr$ more than that of the bus, then what is the speed of bus per hour?
  1. $60\ km$
  2. $75\ km$
  3. $55\ km$
  4. $45\ km$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let speed of bus be v. Speed of train = v + 15. Time = distance / speed. 900/v - 900/(v+15) = 5. Dividing by 5: 180/v - 180/(v+15) = 1. 180(v+15-v) = v(v+15). 2700 = v^2 + 15v. v^2 + 15v - 2700 = 0. (v+60)(v-45) = 0. v = 45.

Multiple choice

Arunoday started walking towards his office at $9 AM$ in the morning. He reached his office at $9:30AM$. He started walking again to reach home in same time. What is the total distance covered by Arunoday if the average speed of Arunoday is $4 km/hr$?
  1. $2 km $
  2. $4 km $
  3. $6 km $
  4. $8 km $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Arunoday walks to the office in 30 minutes (0.5 hours) at 4 km/hr, covering 2 km. He walks back home in the same time, covering another 2 km. Total distance = 2 + 2 = 4 km.

Multiple choice

A particle covers half of its total distance with speed $v_{1}$ and the rest half distance with speed $v_{2}$. Its average speed during the complete journey is :
  1. $\dfrac{v_{1}+v_{2}}{2}$
  2. $\dfrac{v_{1}v_{2}}{v_{1}+v_{2}}$
  3. $\dfrac{2v_{1}v_{2}}{v_{1}+v_{2}}$
  4. $\dfrac{v_{1}^{2}v_{2}^{2}}{v_{1}^{2}+v_{2}^{2}}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average speed = Total distance / Total time. Let total distance be 2d. 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

An aeroplane travels a distance in the form of a square with the speeds of 400 km/hr. 600 km/hr, 800 km/hr and 1,200 km/hr respectively. Find the average speed for the whole distance along the four sides of the square.

  1. 640 km/hr

  2. 620 km/hr

  3. 630 km/hr

  4. 650 km/hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Average speed for a square path with sides of length L is total distance (4L) divided by total time. Time = L/400 + L/600 + L/800 + L/1200. Common denominator is 2400. Time = L(6+4+3+2)/2400 = 15L/2400 = L/160. Average speed = 4L / (L/160) = 4 * 160 = 640 km/hr.

Multiple choice

A car travels the first half of the distance between two places with a speed of $60kmp$. The speed of the car for the rest of the distance so that its average speed becomes $90kmph$.
  1. $60\ kmph$
  2. $90\ kmph$
  3. $120\ kmph$
  4. $180\ kmph$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the total distance be 2d. The total time is d/60 + d/v, while the average speed is 90 kmph. Thus 2d/(d/60 + d/v) = 90, which gives v = 180 kmph. Equal distances require using the harmonic mean, not the ordinary arithmetic mean.

Multiple choice

If a car covers $\dfrac{2}{5^{th}}$ of the total distance with $v_{1}$ speed and $\dfrac{3}{5^{th}}$ distance with $v_{2}$ then average speed:
  1.  $\dfrac{1}{2}\sqrt{v_{1}v_{2}}$
  2. $\dfrac{v_{1}+v_{2}}{2}$
  3.  $\dfrac{2v_{1}v_{2}}{v_{1}+v_{2}}$
  4. $\dfrac{5v_{1}v_{2}}{3v_{1}+2v_{2}}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Average speed = Total distance / Total time. Let total distance be D. Time t1 = (2D/5) / v1 and t2 = (3D/5) / v2. Total time = (2D/5v1) + (3D/5v2) = (2Dv2 + 3Dv1) / (5v1v2). Average speed = D / [(2Dv2 + 3Dv1) / (5v1v2)] = 5v1v2 / (3v1 + 2v2).

Multiple choice

A particle is constrained to move on a straight line path. It returns to the starting point after $10sec$. The total distance covered by the particle during this time is $30m$. Which of the following statements about the motion of the particle is true?

  1. Displacement of the particle is zero
  2. Average speed of the particle is $3m/s$
  3. Displacement of the particle is $30m$

  4. both (a) and (b)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Displacement is the change in position. Since the particle returns to the starting point, displacement is 0. Average speed is total distance / total time = 30m / 10s = 3m/s. Both statements are true.