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

Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?

  1. 9 a.m.

  2. 10 a.m.

  3. 10.30 a.m.

  4. 11 a.m.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

At 8 a.m., train A has traveled 20 km. Remaining distance = 110 - 20 = 90 km. Relative speed = 20 + 25 = 45 kmph. Time to meet = 90 / 45 = 2 hours. 8 a.m. + 2 hours = 10 a.m.

Multiple choice

Points $A$ and $B$ on a national highway are at a distance of $120 km$ from each other. One car starts from $A$ and another from $B$ at the same time. The car which starts from $A$ moves with a constant speed along the direction $AB$ and the second moves with a constant speed in the same direction from $B$. The first car overtakes the second car in $4$ hours. However, if the second car moves from $B$ towards $A$ then the two meet each other after $2$ hours. Find the speed of the car which starts from $A$.
  1. $45 {km}/{hr}$
  2. $65 {km}/{hr}$
  3. $85 {km}/{hr}$

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

Let speeds be v1 and v2. Case 1 (same direction): 120 = (v1 - v2) * 4 => v1 - v2 = 30. Case 2 (opposite direction): 120 = (v1 + v2) * 2 => v1 + v2 = 60. Adding the equations: 2*v1 = 90 => v1 = 45 km/hr.

Multiple choice

Two trains each $200$ m long move towards each other on parallel lines with velocities $20$ kmph and $30$ kmph respectively. What is the time that elapses when they first meet until they have cleared each other?
  1. $20$ s
  2. $24.8$ s
  3. $28.8$ s
  4. $30$ s
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Relative speed = 20 + 30 = 50 km/h = 50 * (5/18) m/s = 250/18 m/s. Total distance to cover = 200 + 200 = 400 m. Time = Distance / Speed = 400 / (250/18) = 400 * 18 / 250 = 1.6 * 18 = 28.8 seconds.

Multiple choice

Places $P_1$ and $P_2$ are $250$ km apart from each other on a national highway. A car starts from $P_1$ and another from $P_2$ at the same time. If they go in the same direction then they meet in $5$ hours and if they go in opposite directions they meet in $\displaystyle \frac{25}{13}$ hours. The speed of the cars are __________.
  1. $90$ km/hr, $40$ km/hr
  2. $40$ km/hr, $80$ km/hr
  3. $20$ km/hr, $60$ km/hr
  4. $50$ km/hr, $12$ km/hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let speeds be u and v. Same direction: (u-v) = 250/5 = 50. Opposite direction: (u+v) = 250 / (25/13) = 250 * 13 / 25 = 130. Adding equations: 2u = 180, u = 90. Then v = 40.

Multiple choice

A man travels $370$km partly by train and partly by car. If he covers $250$km by train and the rest by car, it takes him $4$ hours. But, if he travels $130$ km by train and the rest by car, he takes $18$ minutes longer. Find the speed of the train and car respectively.
  1. $80$ km/hr, $100$ km/hr
  2. $98$ km/hr, $100$ km/hr
  3. $100$ km/hr, $98$ km/hr
  4. $100$ km/hr, $80$ km/hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let train speed be x and car speed be y. We have 250/x + 120/y = 4 and 130/x + 240/y = 4.3. Solving this system of equations yields x=100 and y=80.

Multiple choice

Two trains start at the same time from A and B and proceed toward each other at the speed of $75$ km hr and $50$ km/hr respectively. When both meet at a point in between, one train was found to have travelled $175$ km more than the other. Find the distance between A and B.
  1. $875$ km
  2. $785$ km
  3. $758$ km
  4. $857$ km
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Speeds 75 and 50. Ratio of distances = 75/50 = 3/2. Let distances be 3x and 2x. 3x - 2x = 175 => x = 175. Total distance = 3x + 2x = 5x = 5 * 175 = 875 km.

Multiple choice

Speed of boat in still water is $5\ \text{ km/h}$. The river is flowing with a speed of $2\ \text{km/h}$ and time taken to cover a certain distance upstream is $2$ h more than time taken to cover the same distance downstream. Find the distance.
  1. $10.5\ \text{ km}$
  2. $11\ \text{km}$
  3. $10.9\ \text{km}$
  4. $15\ \text{km}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let distance be D. Upstream speed = 5-2 = 3 km/hr. Downstream speed = 5+2 = 7 km/hr. D/3 - D/7 = 2. (7D - 3D) / 21 = 2. 4D = 42, so D = 10.5 km.

Multiple choice

Points A and Bare 80 km. apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction, they meet in 8 hours and if they move in opposite directions, they meet in one hour and twenty minutes. Find the speeds of the two cars

  1. 55 km/h & 35 km/hr

  2. 50 km/h & 35 km/hr

  3. 70 km/h & 60 km/hr

  4. 35 km/h & 25 km/hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let speeds be x and y. Same direction: 80 / (x-y) = 8 => x-y = 10. Opposite direction: 80 / (x+y) = 4/3 => x+y = 60. Solving: 2x = 70 => x = 35, y = 25.

Multiple choice

A thief escaped from police custody. Since he was sprinter he could clock $40 km/hr$. The police realized it after $3$ hr and started chasing him in the same direction at $50 km/hr$. The distance travelled by police is equal to
  1. $20 km$
  2. $600 km$
  3. $660 km$
  4. $360 km$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Thief travels for 3 hours at 40 km/hr = 120 km lead. Relative speed = 50 - 40 = 10 km/hr. Time to catch = 120 / 10 = 12 hours. Distance traveled by police = 50 km/hr * 12 hr = 600 km.

Multiple choice

Two trains start simultaneously from two stations $300$ km apart and move towards each other.The speed of one train is more than the other by $20$ km/hr. If the distance between the trains after two hours is $20$ km, find the speeds of the trains.
  1. Speed of the first train is $40$ km/hr and Speed of the second train is $60$ km/hr
  2. Speed of the first train is $60$ km/hr and Speed of the second train is $80$ km/hr
  3. Speed of the first train is $100$ km/hr and Speed of the second train is $80$ km/hr
  4. Speed of the first train is $70$ km/hr and Speed of the second train is $90$ km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the speeds be v and v+20. In 2 hours, the trains cover a combined distance of 300 - 20 = 280 km. Thus, 2(v + v + 20) = 280, which simplifies to 2v + 20 = 140, so 2v = 120 and v = 60. The speeds are 60 km/hr and 80 km/hr.