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 man reduces his speed to two third to walk a distance and consequently becomes late by 1 hour With his usual speed he covers the same distance in
  1. $\displaystyle \frac{1}{4}$ hour
  2. $\displaystyle \frac{1}{2}$ hour

  3. 2 hours
  4. $\displaystyle 1\frac{1}{2}$ hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let usual speed be v and distance be d. Usual time t = d/v. New speed = (2/3)v. New time = d / ((2/3)v) = (3/2)t. We are given (3/2)t - t = 1 hour, so (1/2)t = 1, t = 2 hours.

Multiple choice

A hare sees a dog $200$ m away from her and scuds off in the opposite direction at a speed of $24$ km/hr. Two minutes later the dog perceives her and gives chase at a speed of $32$ km/hr How soon will the dog overtake hare and what is the distance from the spot from where the hare took flight?
  1. $8$ min, $2$ km
  2. $\displaystyle 7\frac{1}{2}$ min, $2$ km
  3. $\displaystyle 7\frac{1}{2}$ min, $3$ km
  4. $\displaystyle 7\frac{1}{2}$ min, $1$ km
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Train A leaves Ludhiana for Delhi at 11 am running at a speed of 60 km/hr. Train B leaves Ludhiana for Delhi by the same route at 2 pm on the same day, running at a speed of 72 km/hr. At what time will the two trains meet each other ?

  1. 5 am on the next day

  2. 2 am on the next day

  3. 5 pm on the next day

  4. 2 pm on the next day
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Train A travels for 3 hours before Train B starts, covering 60 * 3 = 180 km. Relative speed = 72 - 60 = 12 km/hr. Time to catch up = 180 / 12 = 15 hours. 15 hours after 2 pm is 5 am the next day.

Multiple choice

A boat takes 11 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream be 3 km/hr and the speed of the boat in still water be `12 km/hr, then what is the distance between A and B ?
  1. $100$ km
  2. $90$ km
  3. $110$ km
  4. $120$ km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let distance AB = D. Downstream speed = 12+3 = 15 km/hr. Upstream speed = 12-3 = 9 km/hr. Time = D/15 + (D/2)/9 = 11. D/15 + D/18 = 11. (6D + 5D)/90 = 11. 11D/90 = 11. D = 90 km.

Multiple choice

A boat takes $90$ minutes less to travel $36$ km downstream than to travel the same distance upstream. If the speed of the boat in still water is $10$ km/hr, then what is the speed of the stream ?
  1. $4$ km/hr
  2. $3$ km/hr
  3. $2.5$ km/hr
  4. $2$ km/hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let s be stream speed. Time upstream = 36/(10-s), time downstream = 36/(10+s). Given 36/(10-s) - 36/(10+s) = 1.5 hours (90 mins). Solving 36(10+s - 10+s)/(100-s^2) = 1.5 leads to 72s = 1.5(100-s^2), which simplifies to s^2 + 48s - 100 = 0. Solving gives s = 2.

Multiple choice

Distance between two points A and B is 110 km A motor cycle rider starts from A towards B at 7 am at a speed of 20 km/hr. Another motor cycle rider starts from B towards A at 8 am at a speed of 25 km/hr. Find when will they cross each other.

  1. 11 am

  2. 9 : 30 am

  3. 8 : 30 am

  4. 10 am
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

At 8 am, the first rider has traveled 20 km. Remaining distance = 110 - 20 = 90 km. Relative speed = 20 + 25 = 45 km/hr. Time to meet = 90 / 45 = 2 hours after 8 am, which is 10 am.

Multiple choice

A train leaves the station $1$ hour before the scheduled time. The driver decreases its speed by $50$ km/hr. At the next station $300$ km away the train reached on time. Find the original speed of the train.
  1. $100$ km/hr
  2. $150$ km/hr
  3. $125$ km/hr
  4. $200$ km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let original speed be v. Time taken at original speed is 300/v. Time taken at reduced speed (v-50) is 300/(v-50). The difference is 1 hour: 300/(v-50) - 300/v = 1. Solving v^2 - 50v - 15000 = 0 gives (v-150)(v+100)=0, so v=150.

Multiple choice

I started on my bicycle at $7$ A.M. to reach a certain place. After going a certain distance, my bicycle went out of order. Consequently, I rested for $35$ minutes and came back to my house walking all the way. I reached my house at $1$ P.M. If my cycling speed is $10$ km/hr and my walking speed is $1$ km/hr, then what distance did I cover on my bicycle?
  1. $\displaystyle 3\frac{61}{66}$ km
  2. $\displaystyle 4\frac{61}{66}$ km
  3. $\displaystyle 6\frac{61}{66}$ km
  4. $\displaystyle 7\frac{61}{66}$ km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let distance be D. Cycling time = D/10. Walking time = D/1. Total time = 6 hours (7 AM to 1 PM). Total time = D/10 + D/1 + 35/60 = 6. 11D/10 = 6 - 7/12 = 65/12. D = 65/12 * 10/11 = 650/132 = 325/66 = 4 61/66 km.

Multiple choice

The ratio between the rates of walking of $A$ and $B$ is $2 : 3$ and therefore $A$ takes $10$ minutes more than the time taken by $B$ to reach the destination. If $A$ had walked at double the speed, then in what time would he have covered that distance?
  1. $10$ minutes
  2. $12$ minutes
  3. $15$ minutes
  4. $18$ minutes
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ratio of speeds A:B = 2:3, so ratio of times A:B = 3:2. Let times be 3t and 2t. 3t - 2t = 10, so t = 10. A's time = 30 minutes. If speed is doubled, time is halved: 30 / 2 = 15 minutes.

Multiple choice

$A$ and $B$ walk from $X$ to $Y$, a distance of $27$ km, at $5$ km/hr and $7$ km/hr, respectively. $B$ reaches $Y$ and immediately turns back meeting $A$ to $Z$. What is the distance from $X$ to $Z $?
  1. $22.5 $ km
  2. $20.0$ km
  3. $25.0 $ km
  4. $24.5 $ km
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A and B travel 27 km. B reaches Y (27 km) and turns back. When they meet at Z, the total distance covered by both is 27 + 27 = 54 km. The time taken is 54 / (5 + 7) = 4.5 hours. The distance from X to Z is the distance A travels in 4.5 hours, which is 5 * 4.5 = 22.5 km.