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

A man covers a distance of 200 km in 4 hours partly by train and partly by car. If the speed of the train is 40 km/h and the speed of the car is 60 km/h, how much distance did he travel by car?

  1. 50 km

  2. 100 km

  3. 120 km

  4. 150 km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the distance by train and (200-x) be the distance by car. Time = x/40 + (200-x)/60 = 4. Multiply by 120: 3x + 2(200-x) = 480. 3x + 400 - 2x = 480, so x = 80. Distance by car = 200 - 80 = 120 km.

Multiple choice

Two places P and Q are 216 km apart and connected by a straight road. Ramesh travels from P to Q, while Suresh travels from Q to P. Starting at the same time, they meet each other after exactly 1 hour and 20 minutes. If Ramesh reaches Q exactly 36 minutes after Suresh reaches P, what is Ramesh's speed in km per hour?

  1. 64 km/h

  2. 68 km/h

  3. 72 km/h

  4. 82 km/h

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

Let speeds be R and S. Relative speed = 216 / (4/3) = 162 km/h. So R + S = 162. Time taken by Ramesh = 216/R, by Suresh = 216/S. Given 216/R = 216/S + 36/60. Solving the system yields R = 72.

Multiple choice

A train departs a station daily at 6:00 am and follows a fixed schedule. One day, it traveled at a constant speed of 50 km per hour and arrived at its destination 6 hours later than its scheduled time. The next day, it traveled three-fourths of its route in one-half of its total scheduled travel time, and the remaining distance at 40 km per hour to reach just on time. The scheduled arrival time of the train is:

  1. 4:00 pm

  2. 5:00 pm

  3. 6:00 pm

  4. 7:00 pm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let D be distance and T be scheduled time. Day 1: D/50 = T + 6. Day 2: (3/4)D / (T/2) = speed1, and (1/4)D / (T_rem) = 40. Solving the system of equations for the scheduled arrival time relative to 6:00 am yields 4:00 pm.

Multiple choice

When will a hiker reach the summit of a mountain located 12 miles away if he starts at 7:00 AM, maintains a speed of 3 miles per hour for the first half of the distance, takes a 40-minute break, and then reduces his pace to 2 miles per hour due to increasing elevation?

  1. 12:40 PM

  2. 1:00 PM

  3. 1:40 PM

  4. 2:30 PM

  5. 3:10 PM
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The first 6 miles (half distance) at 3 mph takes 2 hours. Adding the 40-minute break, the time elapsed is 2 hours 40 minutes. The remaining 6 miles at 2 mph takes 3 hours. Total time is 5 hours 40 minutes from 7:00 AM, which is 12:40 PM.

Multiple choice

A train travels from Station A to Station B at a speed of 80 miles per hour. On the return journey, due to track repairs, the train travels at a reduced speed of 60 miles per hour. If the total time for the round trip is 3.5 hours, how far is Station B from Station A?

  1. 120 miles

  2. 150 miles

  3. 180 miles

  4. 240 miles

  5. 250 miles
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let distance be D. Time = D/80 + D/60 = 3.5. (3D+4D)/240 = 3.5. 7D/240 = 3.5. D = 3.5 * 240 / 7 = 0.5 * 240 = 120 miles.

Multiple choice

A truck covers a distance of 240 miles on its outbound journey at a speed of 120 miles per hour. For the return trip over the same route, its speed drops to 80 miles per hour due to congestion. What is the truck's overall average speed for the complete round trip?

  1. 82 miles per hour

  2. 84 miles per hour

  3. 88 miles per hour

  4. 96 miles per hour

  5. 98 miles per hour
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Average speed = Total distance / Total time. Total distance = 240 + 240 = 480 miles. Time out = 240 / 120 = 2 hours. Time back = 240 / 80 = 3 hours. Total time = 5 hours. Average speed = 480 / 5 = 96 mph.

Multiple choice

A bus covers a certain distance at the speed of 45 km/hr to reach a petrol pump and returns back at the rate of 30 km/hr to initial position. The whole journey takes 3 hours and 45 minutes. What is the distance travelled by the bus from the petrol pump to the initial position?

  1. 67.5 km

  2. 85.5 km

  3. 68.9 km

  4. 55.7 km

  5. 25.5 km
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let distance be D. Total time = D/45 + D/30 = 3.75 hours. (2D + 3D) / 90 = 3.75. 5D = 337.5. D = 67.5 km.

Multiple choice

A and B started simultaneously from M and N towards N and M, respectively. If the speed of A is 50% more than that of B, they can meet at 180 km from M. At what distance from N will they meet if the speed of A is twice that of B?

  1. 240 km

  2. 200 km

  3. 120 km

  4. 100 km

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let speed of B be v, A be 1.5v. They meet at 180 km from M. Distance MN = D. A travels 180, B travels D-180. Time is same: 180/(1.5v) = (D-180)/v. 120 = D-180 => D=300. Case 2: A speed 2v, B speed v. A travels x, B travels 300-x. x/(2v) = (300-x)/v. x = 600-2x => 3x=600 => x=200. Distance from N = 300-200 = 100 km.

Multiple choice

Car A started from Washington at a speed of 40 kmph and two hours later, Car B also started from the same point towards the same destination at a speed of 60 kmph. Car C started following Car B two hours later. If all the three cars reach Washington at the same time, what is the speed of Car C?

  1. 80 kmph

  2. 100 kmph

  3. 108 kmph

  4. 120 kmph

  5. 125 kmph
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let D be the distance. Time for A = D/40. Time for B = D/60 + 2. Time for C = D/V + 4. Since they arrive at the same time, D/40 = D/60 + 2 => D/120 = 2 => D = 240 km. For C, D/V + 4 = 240/40 = 6 => 240/V = 2 => V = 120 kmph.

Multiple choice

Directions for question: M and N start from X towards Y at 8 am with speeds 60 kmph and 50 kmph, respectively. After reaching Y, they spend 1 hour (individually) and then go back to X. M meets N at 30 km from Y, when M was returning to X, while N is still going to Y. What is the distance between X and Y?

  1. 550 km

  2. 600 km

  3. 630 km

  4. 1100 km

  5. cannot be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance be D. M travels D + 30 km, N travels D - 30 km. M's speed = 60, N's speed = 50. Time taken by M = (D+30)/60 + 1 (break). Time taken by N = (D-30)/50. Since they meet when N is still going to Y, the times are equal. (D+30)/60 + 1 = (D-30)/50. (D+90)/60 = (D-30)/50. 5D + 450 = 6D - 180. D = 630 km.

Multiple choice

Towns X and Y are separated by a 90 km highway. Rahul departs from X towards Y, while Rohan starts from Y towards X, both setting off at the same time. They cross paths exactly 2 hours after their journey begins. After meeting, Rahul reaches Y, 180 minutes later than Rohan reaches X. Determine the speed of Rahul in km/hr.

  1. 15

  2. 18

  3. 20

  4. 22

  5. 24
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let speeds be Vr and Ro. They meet in 2 hours, so 2(Vr + Ro) = 90, Vr + Ro = 45. After meeting, Rahul takes time t1 = (Distance_Y_to_X) / Vr = (Ro * 2) / Vr. Rohan takes t2 = (Distance_X_to_Y) / Ro = (Vr * 2) / Ro. Given t1 = t2 + 3, solve the system of equations to find Vr = 15.

Multiple choice

A cargo ship X takes (d - 6) hours to travel a certain distance downstream and (d + 6) hours to travel the same distance upstream. The speed of ship X in still water is 20 km/hr. Another cargo ship Y has a speed in still water equal to the speed of the river current, which is 8 km/hr. Find the distance (in km) covered by ship Y downstream in (d + 4) hours, assuming both ships are operating in the same river conditions.

  1. 245 km

  2. 258 km

  3. 285 km

  4. 304 km

  5. 348 km
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let distance be D. Downstream speed = 20+8=28. Upstream = 20-8=12. D/28 = d-6, D/12 = d+6. D = 28(d-6) = 12(d+6). 28d - 168 = 12d + 72. 16d = 240. d = 15. D = 28 * (15-6) = 28 * 9 = 252. Ship Y speed = 8. Downstream = 8+8=16. Distance in (d+4) = 15+4=19 hours. Distance = 16 * 19 = 304.

Multiple choice

The distance between cities A and B is 120 miles. A car travels from A to B at 60 miles per hour and returns from B to A along the same route at 40 miles per hour. What is the average speed for the round trip?

  1. 48

  2. 50

  3. 52

  4. 56

  5. 58
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Average speed = Total Distance / Total Time. Total distance = 120 + 120 = 240 miles. Time 1 = 120/60 = 2 hours. Time 2 = 120/40 = 3 hours. Total time = 5 hours. Average speed = 240 / 5 = 48 mph.