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

Rahul starts travelling at the speed of 50 kmph from A to B, 180 km apart. The speed of Rahul decreases by 10% every hour. What is the total time taken by Rahul to go from A to B?

  1. 4.25 h

  2. 5.15 h

  3. 5.75 h

  4. 6.15 h

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

Rahul travels 50 km in the first hour, 45 km in the second, 40.5 km in the third, and 36.45 km in the fourth. Total distance covered in 4 hours is 171.95 km. The remaining 8.05 km is covered at a speed of 32.805 km/h, taking approximately 0.245 hours, totaling 4.245 hours.

Multiple choice

Anna and Britney start walking from city A to city B at the same time. The distance between the cities A and B is 60 kilometres. Anna travels 4 kmph slower than Britney. When Britney reaches city B, she at once turns back, meeting Anna 12 km away from city B. Which of the following could be the speed of Britney?

  1. 8 kmph

  2. 12 kmph

  3. 16 kmph

  4. 15 kmph
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Britney's speed be v and Anna's be v-4. Britney travels 60 km and then returns 12 km, total 72 km. Anna travels 60 - 12 = 48 km. Since times are equal, 72/v = 48/(v-4). Solving gives 72v - 288 = 48v, so 24v = 288, v = 12.

Multiple choice

There is a single road between two cities P and Q. Two buses start running from these cities P and Q towards each other with speeds of 90 kmph and 108 kmph, individually. What will be the distance between the two buses 10 s before they come face to face?

  1. 550 m

  2. 330 m

  3. 440 m

  4. 660 m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Relative speed = 90 + 108 = 198 kmph. Convert to m/s: 198 * (5/18) = 55 m/s. In 10 seconds, the distance covered is 55 * 10 = 550 m. This is the distance between them 10 seconds before they meet.

Multiple choice

A train running with a speed of x km/hr covers a certain distance in y hours. If its speed is increased by 12 km/hr, then it will cover the same distance in 2 hours less than the scheduled time. But if its speed is decreased by 10 km/hr, then it will take 3 hours more than the scheduled time. Which of the following is the correct set of equations representing this situation?

  1. x - 6y = -12; 3x - 10y = -30

  2. 3x - 6y = 30; x - 10y = -12

  3. x - 3y = 12; x - 13y = 30

  4. x - 6y = -12; 3x - 10y = 30
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Distance D = xy. (x+12)(y-2) = xy => xy - 2x + 12y - 24 = xy => -2x + 12y = 24 => x - 6y = -12. (x-10)(y+3) = xy => xy + 3x - 10y - 30 = xy => 3x - 10y = 30.

Multiple choice

Robin lives 33 miles from his place of work. He rides his bike at a speed of 6 mph from his house to the metro station. He then takes the metro to work, which travels at 30 mph. If he spends 6 minutes less on metro than on his bike, then what is the distance from the metro to his house?

  1. 4 miles

  2. 6 miles

  3. 8 miles

  4. 12 miles
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let d be the distance by bike. Then 33 - d is the distance by metro. Time by bike = d/6. Time by metro = (33 - d)/30. Given d/6 - (33 - d)/30 = 6/60 = 0.1. Multiply by 30: 5d - (33 - d) = 3. 6d = 36, so d = 6 miles.

Multiple choice

A truck covers a distance of 384 km at a certain speed. If the speed is decreased by 16 km/h, it will take 2 hours more to cover the same distance. 75% of its original speed (in km/h) is

  1. 45

  2. 54

  3. 48

  4. 42
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speed be v. 384/(v-16) - 384/v = 2. Solving for v: 384v - 384(v-16) = 2v(v-16). 384 * 16 = 2v^2 - 32v. v^2 - 16v - 3072 = 0. Roots are (16 +/- sqrt(256 + 12288))/2 = (16 +/- 112)/2. v = 64. 75% of 64 is 48.

Multiple choice

A certain distance is covered at a certain speed (s1). If half of this distance is covered in double the time at speed (s2). Find the ratio of the two speeds. Also, if s1 is 60 km/hr, then find s2.

  1. 1 : 16, 3.75 km/hr

  2. 4 : 1, 15 km/hr

  3. 2 : 1, 30 km/hr

  4. 2 : 8, 240 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Distance D at speed s1 takes time t = D/s1. Half distance D/2 at speed s2 takes time 2t. So s2 = (D/2) / (2t) = D / (4t) = (D/t) / 4 = s1 / 4. Thus s1/s2 = 4/1. If s1 = 60, s2 = 15.