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

The distance between two cities $A$ and $B$ is $330\ km$. A train starts from $A$ at $8\ a.m.$ and travels towards $B$ at $60\ km/hr$. Another train starts from $B$ to $9\ a.m.$ and travels towards $A$ at $75\ km/hr$. At what time do they meet?
  1. $10\ a.m.$
  2. $10:30\ a.m.$
  3. $11\ a.m.$
  4. $11:30\ a.m.$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Train A travels for 1 hour alone (8am to 9am), covering 60 km. Remaining distance = 330 - 60 = 270 km. Relative speed = 60 + 75 = 135 km/hr. Time to meet = 270 / 135 = 2 hours after 9am, which is 11am.

Multiple choice

A man drives his car on the highway where the speed limit is $60$ kmph. He has to cover a distance of $240$ km at a uniform speed on the road. If he increases his speed by $20$ kmph, he can reach the destination 1 hour earlier. What is his original speed?
  1. $20$ kmph
  2. $5$ kmph
  3. $60$ kmph
  4. $30$ kmph
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let original speed be v. Time taken = 240/v. New time = 240/(v+20). Difference = 1 hour. 240/v - 240/(v+20) = 1. 240(v+20 - v) = v(v+20). 4800 = v^2 + 20v. v^2 + 20v - 4800 = 0. (v+80)(v-60) = 0. Original speed is 60 kmph.

Multiple choice

A plane left $40$ minutes late due to bad weather and in order to reach its destination, $1600$ km away in time, it had to increase its speed by $400$km/hr from its usual speed. Find the usual speed of the plane.
  1. $1000\text{km/h}$
  2. $1600\text{km/h}$
  3. $800\text{km/h}$
  4. $600\text{km/h}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let v be the usual speed. Time taken at usual speed is 1600/v, and at increased speed is 1600/(v+400). The difference is 40 minutes (2/3 hours). Solving 1600/v - 1600/(v+400) = 2/3 leads to v^2 + 400v - 960000 = 0. Factoring gives (v+1200)(v-800) = 0, so v = 800 km/h.

Multiple choice

An aeroplane started $30$ minutes later than the schedule time from a place $1500km$ away from its destination to reach the destination at the schedule time the pilot had to increase the speed by $250$km/hr what was the speed of the aeroplane per hour during the journey?
  1. $100$km/hr
  2. $1000$km/hr
  3. $1050$km/hr
  4. $900$km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let v be the original speed. The time taken is 1500/v. With increased speed, time is 1500/(v+250). The difference is 0.5 hours. Solving 1500/v - 1500/(v+250) = 0.5 leads to v^2 + 250v - 750000 = 0. Factoring gives (v+1000)(v-750) = 0, so v = 750. The new speed is 750 + 250 = 1000 km/hr.

Multiple choice

The ratio of the speeds of Amar, Akabar and antony is $8:5:4$. If Akbar takes $15$min more than Amar to cover a certain distance, find the time taken by Antony to cover the same distance.
  1. $30$ minutes
  2. $60$ minutes
  3. $40$ minutes
  4. $50$ minutes
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Speed ratio = 8:5:4. Time ratio = 1/8 : 1/5 : 1/4 = 5:8:10. Let times be 5x, 8x, 10x. Akbar takes 15 min more than Amar: 8x - 5x = 15 => 3x = 15 => x = 5. Antony's time = 10x = 50 minutes.