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

Alexander and Bennett plan to meet at a cinema hall. Alexander leaves his office at 4:00 pm at a speed of 20 miles per hour. Bennett leaves his office at 5:00 pm at a speed of 40 miles per hour. Both Alexander and Bennett reach the cinema hall at the same time. Quantity A Distance of Alexander's office from the cinema hall Quantity B Distance of Bennett's office from the cinema hall

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

A motorboat takes 6 hours to cover 100 km downstream and 30 km upstream. If the boat goes 75 km downstream and returns back to starting point in 8 hours, the speed of the boat in still water is:

  1. 22 km/hr

  2. 20 km/hr

  3. 24 km/hr

  4. 30 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let boat speed be b and stream speed be s. 100/(b+s) + 30/(b-s) = 6. 75/(b+s) + 75/(b-s) = 8. Let u = 1/(b+s) and v = 1/(b-s). 100u + 30v = 6 and 75u + 75v = 8. Solving gives b = 20, s = 5.

Multiple choice

The distance between station A and B by road is 240 km and by train it is 300 km. A car starts from station A with a speed of x km/hr whereas a train starts from station B with a speed 20 km/hr more than the speed of the car. If the time taken by the train is 1 hour less than that taken by the car, then the quadratic equation formed is:

  1. x2 + 80x - 6000 = 0

  2. x2 + 80x - 4800 = 0

  3. x2 + 240x - 1600 = 0

  4. x2 - 80x + 4800 = 0
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Time for car = 240/x. Time for train = 300/(x+20). Given 240/x - 300/(x+20) = 1. 240(x+20) - 300x = x(x+20). 240x + 4800 - 300x = x^2 + 20x. x^2 + 80x - 4800 = 0.

Multiple choice

The distance between station A and B by road is 240 km and by train it is 300 km. A car starts from station A with a speed of x km/hr whereas a train starts from station B with a speed 20 km/hr more than the speed of the car. If the time taken by train is 1 hour less than that taken by the car, the speed of the car is:

  1. 60 km/hr

  2. 120 km/hr

  3. 40 km/hr

  4. 80 km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The time taken by the car is 240/x hours, and the time taken by the train is 300/(x + 20) hours. We are given that the train's time is 1 hour less than the car's time, so 240/x - 300/(x + 20) = 1. Solving this equation or testing the options gives x = 40 km/hr.

Multiple choice

Pankaj travelled a certain part of the journey with speed 5 km/h and then he took an auto travelling at 25 km/h for the remaining part of the journey. He took 10 hours for the entire journey. What distance did he travelled by auto if the average speed of the entire journey be 17 km/h.

  1. 750 km

  2. 100 km

  3. 150 km

  4. 200 km

  5. 250 km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

With an average speed of 17 km/h over 10 hours, the total distance travelled is 170 km. Let t be the time spent in the auto; then the time spent walking is 10 - t. Solving the distance equation 5*(10 - t) + 25*t = 170 gives 20*t = 120, so t = 6 hours, and the distance by auto is 25 * 6 = 150 km.

Multiple choice

The distance between 2 stations are 800km. One train starts at 5am from A with 62 kmph. Another train starts at 7am from B at 50 kmph. When they will meet?

  1. 12.3pm

  2. 1.30pm

  3. 1.03pm

  4. 2.32pm

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

Train A starts at 5am, covers 62*2 = 124km by 7am. Remaining distance = 800 - 124 = 676km. Relative speed = 62 + 50 = 112 kmph. Time to meet = 676 / 112 = 6.0357 hours. 6 hours 2 minutes approx. 7am + 6h 2m = 1:02pm.

Multiple choice

Two trains X and Y start at the same time in the opposite direction from two points P and Q and arrive at their destinations 36 and 25 hours respectively after their meeting each other. At what speed does the second train Y travel if the first train travels at 80 km/h.

  1. 80 km/hr

  2. 90 km/hr

  3. 70 km/hr

  4. 96 km/hr

  5. 60 km/hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For two objects meeting and then reaching destinations in t1 and t2 time, the ratio of speeds is v1/v2 = sqrt(t2/t1). 80/v2 = sqrt(25/36) = 5/6. v2 = 80 * 6 / 5 = 96 km/h.

Multiple choice

A car goes from A to B in three hours. It stays at B for five hours and then returns to A. If the total time taken in the journey including the stay at B be 12 hrs and the average running speed of the car be 60 km/hr., how far is B from A?

  1. 210 km

  2. 360 km

  3. 420 km

  4. 720 km
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total time is 12 hours, stay is 5 hours, so travel time is 7 hours. Let distance be d. Total distance is 2d. Average speed = Total distance / Total running time. 60 = 2d / 7, so 2d = 420, d = 210 km.

Multiple choice

A rectangular playground measures 120 meters (length) × 119 meters (breadth). If a person travels across its diagonal at a speed of 1 meter per second, then how much time will he take to reach the other corner of the playground?

  1. 1 minute 13 seconds

  2. 2 minutes 27 seconds

  3. 2 minutes 49 seconds

  4. 2 minutes 54 seconds

  5. 3 minutes 25 seconds
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The diagonal length is sqrt(120^2 + 119^2) = sqrt(14400 + 14161) = sqrt(28561) = 169 meters. At 1 m/s, it takes 169 seconds, which is 2 minutes and 49 seconds.

Multiple choice

Mr. Ravi completes a certain journey by a car. If he covered 40% of the distance at the speed of 20kmph, 50% of the distance at 25 kmph and the remaining of the distance at 10 kmph, then what will be the speed?

  1. 15 kmph

  2. 20 kmph

  3. 18 kmph

  4. 14 kmph

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

The average speed is calculated as Total Distance / Total Time. Let the total distance be 100 km; the times are 40/20 = 2 hours, 50/25 = 2 hours, and 10/10 = 1 hour, totaling 5 hours. Average speed = 100 / 5 = 20 kmph.

Multiple choice

Rani started walking to the station half a km from her home at 1 kmph to catch the train in time. After 6 minutes she realized that she had forgotten her purse at home and returned with increased, but constant speed to get it succeeded in catching the train. Find her latter speed in kmph.

  1. 1.5 kmph

  2. 1.2 kmph

  3. 2.2 kmph

  4. 3.5 kmph

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

Distance = 0.5 km. Speed = 1 kmph. Time to station = 0.5 hours = 30 minutes. She walked for 6 minutes (0.1 hours), covering 0.1 km. She is 0.4 km from home. She has 30 - 6 = 24 minutes (0.4 hours) left to return home and reach the station. Total distance to cover = 0.1 (to return) + 0.5 (to station) = 0.6 km. Speed = 0.6 / 0.4 = 1.5 kmph.