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 cyclists Ajay and Sunil are at a distance of 120 km from each other.Both starts at same time speed of Ajay is 12 km/hr while speed of Sunil increases by 1 km/hr every hr with speed being 10 km/hr starting in the first hour , in how many hours will both cyclist meets ?

  1. 3 hrs

  2. 4 hrs

  3. 5 hrs

  4. 8 hrs

  5. 10 hrs
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ajay distance = 12t. Sunil distance = 10 + 11 + 12 + 13 + 14... (sum of arithmetic progression). Total distance = 120. 12t + (t/2)(20 + (t-1)1) = 120. 12t + 10t + 0.5t^2 - 0.5t = 120. 0.5t^2 + 21.5t - 120 = 0. t^2 + 43t - 240 = 0. (t+48)(t-5) = 0. t = 5.

Multiple choice

The ratio of speed of boat in still water to speed of stream is 8 : 5 and total time taken by boat to cover 'D' km distance in downstream and upstream together is 32 hours. Find the time taken by boat to cover '2D' km in still water?

  1. 13 hour

  2. 14.8 hour

  3. 19.5 hour

  4. 12.78 hour

  5. 20.7 hour
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed = 8k, stream = 5k. Downstream = 13k, Upstream = 3k. D/13k + D/3k = 32. D(3+13)/(39k) = 32 => 16D/39k = 32 => D/k = 78. Time for 2D in still water = 2D / 8k = D/4k = 78/4 = 19.5 hours.

Multiple choice

Tom drives around town to run errands. He travels along the four sides of a square-shaped block, with each side measuring 2 miles. Tom starts by driving at a speed of 30 miles per hour (mph), and for each subsequent side of block, he increases his speed by 10 mph until he covers all sides of the block. What is Tom's average speed during this trip?

  1. 39.20 miles per hour

  2. 41.70 miles per hour

  3. 42.10 miles per hour

  4. 46.10 miles per hour
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total distance = 4 sides * 2 miles = 8 miles. Speeds are 30, 40, 50, 60 mph. Time for each side = distance / speed. T1 = 2/30 = 1/15 hr, T2 = 2/40 = 1/20 hr, T3 = 2/50 = 1/25 hr, T4 = 2/60 = 1/30 hr. Total time = (1/15 + 1/20 + 1/25 + 1/30) = (20+15+12+10)/300 = 57/300 = 19/100 hr. Average speed = Total distance / Total time = 8 / (19/100) = 800/19 = 42.105 mph.

Multiple choice

Two hikers, Alex and Emma, start hiking towards each other from two different points, Point X and Point Y, which are 80 kilometres apart. Alex hikes at a speed of 18 km/h for the first 36 kilometres, and then hikes at a speed of 13 km/h for the remaining distance. Emma hikes at a constant speed of 12 km/h throughout the journey. How long will it take for Alex and Emma to meet each other?

  1. 1 hour and 20 minutes

  2. 2 hours and 20 minutes

  3. 2 hours and 40 minutes

  4. 2 hours and 48 minutes
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

A car travels a certain distance at an average speed of 60 km/hr. On the return journey along the same route, the car faces traffic and can only travel at an average speed of 40 km/hr. If the total travel time for the round trip is 6 hours, what is the distance of the route?

  1. 120 km

  2. 124 km

  3. 144 km

  4. 160 km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let d be the one-way distance. Total time = d/60 + d/40 = 6. Multiplying by 120 gives 2d + 3d = 720, so 5d = 720, d = 144 km.

Multiple choice

A runner participates in a marathon and covers one-fourth of the total distance at a speed of 8 km/hr. Out of the total time taken to cover the remaining distance, the runner runs at a speed of 8 km/hr for one-third of the time and at a speed of 6 km/hr for the remaining time. What is the average speed of the runner?

  1. 6.34 km/hr

  2. 6.96 km/hr

  3. 7.56 km/hr

  4. 7.95 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total distance be 12 km. 1/4 (3 km) at 8 km/hr takes 3/8 hours. Remaining 9 km: let total time be T. 1/3 of T at 8 km/hr and 2/3 of T at 6 km/hr. Distance = 8*(T/3) + 6*(2T/3) = 9. 8T/3 + 4T = 9, 20T/3 = 9, T = 27/20 = 1.35 hours. Total time = 0.375 + 1.35 = 1.725 hours. Average speed = 12 / 1.725 = 6.956 km/hr.

Multiple choice

Two friends, Amy and Ben, are at a fitness event held at a circular track with a circumference of 3,500 yards. Amy starts walking clockwise at a speed of 600 yards per minute, and Ben starts walking counterclockwise at a speed of 800 yards per minute. After how much time will Amy and Ben meet each other for the first time, excluding the starting time?

  1. 5 minutes

  2. 4.5 minutes

  3. 3 minutes

  4. 2.5 minutes

  5. 2 minutes
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Relative speed = 600 + 800 = 1400 yards/minute. Distance to cover for first meeting = 3500 yards. Time = 3500 / 1400 = 2.5 minutes.

Multiple choice

The ratio of the speed of a bike to that of a train is 10 : 25. Also, a car covers a distance of 600 miles in 8 hours. The speed of the bike is half the speed of the car. How much distance will the train cover in 6 hours?

  1. 450 miles

  2. 562.5 miles

  3. 662.5 miles

  4. 680 miles

  5. 780 miles
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Car speed = 600 / 8 = 75 mph. Bike speed = 75 / 2 = 37.5 mph. Bike:Train ratio = 10:25 = 2:5. Train speed = (37.5 / 2) * 5 = 93.75 mph. Distance in 6 hours = 93.75 * 6 = 562.5 miles.