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 person goes from point $P$ to point $Q$ covering $1/3$ of the distance with speed $10\ km/hr$, the next $1/3$ of the distance at $20\ km/hr$ and the last $1/3$ of the distance at $60\ km/hr$. The average speed of the person is
  1. $30\ km/hr$
  2. $24\ km/hr$
  3. $18\ km/hr$
  4. $12\ km/hr$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

Multiple choice

A train covers the first $5km$ of its journey at a speed of $30km/hr$ and the next $15km$ at a speed of $45km/hr$. What is the average speed of the train?
  1. $35km/hr$
  2. $37.5km/hr$
  3. $39.5km/hr$
  4. $40km/hr$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Average speed is calculated as the total distance divided by the total time taken. The total distance is 5 km + 15 km = 20 km, and the total time is (5/30) + (15/45) = 1/6 + 1/3 = 1/2 hour, resulting in an average speed of 20 / (1/2) = 40 km/hr.

Multiple choice

An automobile went up a hill at a speed of $10\ km$ an hour and down the same distance at a speed of $20\ km$ an hour. The average speed for the round trip was
  1. $12\dfrac {1}{2} km/ hr$
  2. $13\dfrac {1}{3} km/ hr$
  3. $14\dfrac {1}{2} km/ hr$
  4. $15\ km/ hr$

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

Average speed for a round trip with equal distances is calculated using the harmonic mean formula: 2xy / (x + y). Plugging in 10 and 20 gives 2 * 10 * 20 / (10 + 20) = 400 / 30 = 13 1/3 km/hr.

Multiple choice

A car covers first $2km$ of the total distance of $4km$ with a speed of $30km/h$ and the remaining distance of $2km$ with a speed of $20km/h$. The average speed of the car is:
  1. $24km/h$
  2. $25km/h$
  3. $50km/h$
  4. $26km/h$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Average speed is total distance divided by total time. Total distance is 4 km. Time for first 2 km is 2/30 = 1/15 hours. Time for second 2 km is 2/20 = 1/10 hours. Total time is 1/15 + 1/10 = 5/30 = 1/6 hours. Average speed = 4 / (1/6) = 24 km/h.

Multiple choice

A car travels first $\dfrac{1}{3}$ of the distance AB at $30km/h$,next$\dfrac{1}{3}$ of the distance at $40km/h$ and last $\dfrac{1}{3}$ of the distance at $24km/h$ Its average speed in km/h for the whole journey is
  1. $40$
  2. $35$
  3. $30$
  4. $28$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average speed = Total distance / Total time. Let total distance = 3D. Time = D/30 + D/40 + D/24 = (4D + 3D + 5D) / 120 = 12D/120 = D/10. Average speed = 3D / (D/10) = 30 km/h.

Multiple choice

The distance between two spots A & B, on the same bank of the river ,is $75 km$. Speed of the boat in still water is twice as much as that of the speed of the water current of the river. The boat travels in the river from $A$ to $B$ and returns back to the spot in $16 hour$. What is the speed of the boat in still water?
  1. $12.5 kmph$
  2. $15 kmph$
  3. $16 kmph$
  4. $18 kmph$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let current = x, boat = 2x. Downstream = 3x, Upstream = x. 75/(3x) + 75/x = 16. 25/x + 75/x = 16. 100/x = 16. x = 6.25. Boat speed = 2x = 12.5.

Multiple choice

A car travels a distance of $2000$ m. If the first half distance is covered at $40$ km/ hour and the second half with speed $v$ and the average speed is $48$ km/hour, then the value of $v$ is
  1. $56$ km/hour
  2. $60$ km/hour
  3. $50$ km/hour
  4. $48$ km/h
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average speed = Total distance / Total time. 48 = 2000 / (1000/40 + 1000/v). 48 = 2000 / (25 + 1000/v). 25 + 1000/v = 2000/48 = 41.66. 1000/v = 16.66. v = 1000 / 16.66 = 60.

Multiple choice

A motor vehicle travelled the first third of a distance s at a speed of ${ v }{ 1 }=10$ kmph, the second third at a speed of ${ v }{ 2 }=20$ kmph and the last third at a speed of ${ v }_{ 3 }=60$ kmph. Determine the mean speed of the vehicle over the entire distance s.

  1. 15 kmph

  2. 12 kmph

  3. 10 kmph

  4. 18 kmph
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Mean speed = Total distance / Total time. Let total distance be 3d. Time = d/10 + d/20 + d/60 = (6d+3d+d)/60 = 10d/60 = d/6. Mean speed = 3d / (d/6) = 18 kmph.

Multiple choice

The driver of a train moving with a speed $v_{ 1 }$ sights another train at a distance $s$, ahead of him moving in the same direction with a slower speed $v_{ 2 }$. He applies the brakes and gives a constant deceleration $a$ to his train. For no collision, $s$ is
  1. $=\cfrac { { \left( v_{ 2 }-v_{ 1 } \right) }^{ 2 } }{ 2a } $
  2. $>{ \cfrac{ \left ( v_{ 1 }-v_{ 2 } \right )^2 }{ 2a } }$
  3. $<\cfrac { { \left( v_{ 1 }-v_{ 2 } \right) }^{ 2 } }{ 2a } $
  4. $<\cfrac { v_{ 1 }-v_{ 2 } }{ 2a } $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For no collision, the stopping distance of the first train must be less than the initial distance s plus the distance covered by the second train during the braking time. The relative velocity approach shows s > (v1 - v2)^2 / 2a.