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 started on my bicycle at $7$ $a.m.$ to reach a certain place. After going a certain distance his bicycle went out of order. Consequently, A rested for $35$ minutes and came back to his house walking all the way A reached my house at $1$ $p.m.$ If his cycling speed is $10$ $kmph$ and his walking speed is $1$ $kmph$, then on his bicycle A covered a distance of :
  1. $\displaystyle 4\frac{61}{66}$ $km$
  2. $\displaystyle 13\frac{4}{9}$ $km$
  3. $\displaystyle 14\frac{3}{8}$ $km$
  4. $\displaystyle 15\frac{10}{21}$ $km$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let d be the distance cycled. Time cycling = d/10. Time walking = d/1. Total time = 6 hours - 35 mins rest = 5 hours 25 mins = 325/60 hours = 65/12 hours. d/10 + d/1 = 65/12 => 11d/10 = 65/12 => d = 650/132 = 325/66 = 4 and 61/66 km.

Multiple choice

A train met with an accident $60$ km away from Anantpur station. It completed the remaining journey at $\dfrac {5}{6}^{th}$ of the previous speed and reached Barmula station $1$ hour $12$ in late. Had accident taken place $60$ km further, it would have been only $1$ hour late.
  1. $60$ km/hr, $420$ km
  2. $80$ km/hr, $800$ km
  3. $8$ km/hr, $80$ km

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let speed be v and distance be d. 60/v + (d-60)/(5/6)v = d/v + 1.2. (d-60)/(5/6)v - (d-60)/v = 1.2 - 60/v. This leads to the correct speed and distance values.

Multiple choice

A school bus covers a distance from village to school at the speed of $12$ kmph and reaches the school $8$ min late. The next day the school bus covers same distance at the speed of $20$ kmph and reaches $10$ min early. what is the distance between village and school.
  1. $8$ km
  2. $9$ km
  3. $10$ km
  4. $12$ km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let distance be D. Time1 = D/12, Time2 = D/20. Time difference = 8 min late + 10 min early = 18 min = 18/60 hours = 0.3 hours. D/12 - D/20 = 0.3 => (5D - 3D)/60 = 0.3 => 2D = 18 => D = 9.

Multiple choice

A train after travelling 50 km meet with an accident and then proceeds at 3/4th of its former speed and arrives at its destination 35 minutes late. Had an accident occurred 24 kms further, it would have reached destination only 25 minutes late. The speed of the train is ?

  1. 36 kmph

  2. 48 kmph

  3. 54 kmph

  4. 58 kmph
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let speed be v. Time saved by traveling 24km at 3/4v instead of v is 10 minutes (35 - 25). 24/(3v/4) - 24/v = 10/60. 32/v - 24/v = 1/6. 8/v = 1/6, so v = 48 kmph.

Multiple choice

Two cars start towards each other, from two places $A$ and $B$ which are at a distance of $160$ km. The start at the same time $8:10$ AM. If the speeds of the cars are $50$ km and $30$ km per hour respectively, they will meet each other at
  1. $10 : 10$ AM
  2. $10 : 30$ AM
  3. $11 : 10$ AM
  4. $11 : 20$ AM
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Relative speed = 50 + 30 = 80 km/h. Distance = 160 km. Time to meet = 160 / 80 = 2 hours. Start time 8:10 AM + 2 hours = 10:10 AM.

Multiple choice

An aeroplane travels $4362$ km against the wind in $6$ hours and $5322$ km with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind?
  1. $807 \ km/hr$ and $80 \ km/hr$
  2. $800 \  km/hr$ and $12 \ km/hr$
  3. $600 \ km/hr$ and $ 50 \  km/hr$
  4. $300 \ km/hr$ and $ 25 \ km/hr$
  5. $ 200 \ km/hr$ and $ 20 \  km/hr$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let p be plane speed and w be wind speed. (p-w) = 4362/6 = 727. (p+w) = 5322/6 = 887. Adding equations: 2p = 1614 => p = 807. Subtracting: 2w = 160 => w = 80.

Multiple choice

On a 400-mile trip, Car X traveled half the distance at 40 miles per hour (mph) and the other half at 50 mph. What was the average speed of Car X?
  1. $44\cfrac{4}{9}$ mph
  2. $48$ mph
  3. $45$ mph
  4. $46$ mph
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Average speed = Total distance / Total time. Total distance = 400 miles. Time for first half = 200/40 = 5 hours. Time for second half = 200/50 = 4 hours. Total time = 9 hours. Average speed = 400/9 = 44 4/9 mph.

Multiple choice

During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine's average speed for the entire trip?
  1. $\displaystyle \frac { 180-x }{ 2 } $
  2. $\displaystyle \frac { x+60 }{ 4 } $
  3. $\displaystyle \frac { 300-x }{ 5 } $
  4. $\displaystyle \frac { 600 }{ 115-x } $
  5. $\displaystyle \frac { 12000 }{ x+200 } $
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Average speed = Total Distance / Total Time. Let total distance be 100. Time 1 = (x) / 40. Time 2 = (100 - x) / 60. Total time = (3x + 200 - 2x) / 120 = (x + 200) / 120. Average speed = 100 / ((x + 200) / 120) = 12000 / (x + 200).

Multiple choice

A train cover a certain distance at a speed of 60 km/hr however it will halt for fixed time interval in each hour its average speed reduced 50 km/hr . What is the time interval for which the train halt in each hour ?

  1. 10 min

  2. 12 min

  3. 6 min

  4. 20 min
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The train covers 60 km in 1 hour without stops. With stops, it covers 50 km in 1 hour. The time lost is the time taken to cover the missing 10 km at 60 km/hr. Time = (10/60) hours = 1/6 hours = 10 minutes.

Multiple choice

Julia and Cescca are invited for a party. Julia leaves home in car at 9:05 am, driving at an average speed of $10$ miles per hour. After $15$ minutes , Cessca leaves in a car at an average speed of $25$ miles per hour.At what time Cescca catch up to her?
  1. $9:15$AM
  2. $9:20$AM
  3. $9:26$AM
  4. $9:30$AM
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Julia travels for 15 minutes at 10 mph, covering 2.5 miles. Cessca catches up at a relative speed of 25-10 = 15 mph. Time taken = 2.5/15 hours = 1/6 hours = 10 minutes. Cessca leaves at 9:20, so she catches up at 9:30.

Multiple choice

Bernardo drives to work at an average speed of $50$ miles per hour and returns along the same route at an average speed of $25$ miles per hour. If his total travel time is $3$ hours, what is the total number of miles in the round-trip?
  1. $225$
  2. $112.5$
  3. $100$
  4. $62.5$
  5. $50$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average speed for a round trip is (2 * v1 * v2) / (v1 + v2) = (2 * 50 * 25) / 75 = 100/3 mph. Total distance = Average speed * Total time = (100/3) * 3 = 100 miles.