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

On a two-lane road, car A is travelling with a speed of 36 km $h^{-1}$. Two cars B and C approach car A in opposite directions with a speed of 54 km $h^{-1}$ each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. The minimum required acceleration of car B to avoid an accident is
  1. 1 m $s^{-2}$
  2. 1.5 m $s^{-2}$
  3. 2 m $s^{-2}$
  4. 3 m $s^{-2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Relative speed of B and A is 54 - 36 = 18 km/h = 5 m/s. Relative speed of C and A is 54 + 36 = 90 km/h = 25 m/s. Time for C to reach A is 1000m / 25 m/s = 40s. B must cover 1000m in less than 40s. Using s = ut + 0.5at^2, 1000 = 5 * 40 + 0.5 * a * 40^2. 1000 = 200 + 800a, so 800 = 800a, a = 1 m/s^2.

Multiple choice

A bus is moving with a speed of 10 m $s^{-1}$ on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist with what speed should the scooterist chase the bus?
  1. 40 m $s^{-1}$
  2. 25 m $s^{-1}$
  3. 10 m $s^{-1}$
  4. 20 m $s^{-1}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To overtake the bus in 100 seconds over a distance of 1000 meters, the relative speed of the scooterist with respect to the bus must be 1000 / 100 = 10 m/s. Since the bus is moving at 10 m/s, the scooterist's speed must be 10 + 10 = 20 m/s.

Multiple choice

Two cars are moving in the same direction with the same speed $30km/hr$. They are separated by a distance of $5km$ the speed of a car moving in the opposite direction if it meets these two cars at interval of 4 minutes, will be:
  1. $40km/hr$
  2. $45km/hr$
  3. $30km/hr$
  4. $15km/hr$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The two cars are 5 km apart, and the opposite-moving car meets them 4 minutes apart, or 1/15 hour. Their relative speed is therefore 5 รท (1/15) = 75 km/hr. Since the cars move at 30 km/hr in the opposite direction, the other car's speed is 75 - 30 = 45 km/hr.

Multiple choice

A particle travel half of the distance of a straight journey with a speed $6 m/s$. The remaining part of the distance is covered with speed $2 m/s$ for half of the time remaining journey and with speed $4 m/s$ for other half of time. The average speed of the particle is
  1. $3 m/s$
  2. $4 m/s$
  3. $3/4 m/s$
  4. $5 m/s$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total distance be 2D. First half D at 6 m/s takes time t1 = D/6. Remaining distance D is covered in two halves of time t2. Distance covered = 2*t2 + 4*t2 = 6*t2 = D, so t2 = D/6. Total time = D/6 + 2*(D/6) = D/2. Average speed = 2D / (D/2) = 4 m/s.

Multiple choice

A motor vehicle left the point A and reached the point B by travelling in a straight line for $2$ hours. The vehicle travelled half of the distance at a speed of $v_1=40$ km/h and other half at a speed of $v_2=60$ km/h. The distance between A and B is?
  1. $86$ km
  2. $96$ km
  3. $76$ km
  4. $106$ km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the total distance be 2d. Time taken = d/40 + d/60 = 2 hours. (3d + 2d) / 120 = 2, so 5d / 120 = 2. 5d = 240, d = 48. Total distance 2d = 96 km.