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

To cover a distance of 30 km, Amit takes 2 hours more than Suresh. If Amit doubles his speed, he would take 1 hour less than Suresh. What is Amit`s speed?

  1. 5 km/h

  2. 6 km/h

  3. 6.5 km/h

  4. 7 km/h
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let Amit's speed be v. Time taken = 30/v. Suresh's time = 30/v - 2. If Amit doubles speed (2v), time = 30/2v = 15/v. This is 1 hour less than Suresh, so 15/v = (30/v - 2) - 1. 15/v = 30/v - 3. 3/v = 15/30? No, 3 = 15/v, so v = 5.

Multiple choice

A particle moves on straight path, it returns to starting point after 10 sec. The total distance covered is 30 m then what is not true about the motion of the body?

  1. The displacement of the body is zero.

  2. The average velocity is zero.

  3. The displacement of the body is 30 m.

  4. The average speed of the body is 3m/s.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If the particle returns to the starting point, displacement is 0. Average velocity = displacement / time = 0. Average speed = distance / time = 30 / 10 = 3 m/s. Option C claims displacement is 30m, which is false.

Multiple choice

There was a race between Anand and Rajesh from point 'x' to point 'y' which were 55 km apart. Both started at the same time, Anand at 40 km/hr. After covering a certain distance Anand increased his speed to 50 km/hr and reached 'y' in 1 hour 15 min after leaving 'x'. Rajesh was going with a uniform speed and it took him 1 hour 30 min. What was the distance between Anand and Rajesh when Anand changed his speed?

  1. 2 km

  2. 2.5 km

  3. 3 km

  4. 3.5 km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Anand's total time is 1.25 hours. Let t be the time at 40 km/hr. Distance = 40t + 50(1.25 - t) = 55. 40t + 62.5 - 50t = 55, so 10t = 7.5, t = 0.75 hours. Anand traveled 40 * 0.75 = 30 km before changing speed. Rajesh traveled 30 km at 55/1.5 = 36.67 km/hr. Rajesh's distance = 36.67 * 0.75 = 27.5 km. Difference = 30 - 27.5 = 2.5 km.

Multiple choice

Rita and Mona decided to meet at a fast food joint. The fast food joint is located somewhere between their houses. Both of them started at the same time from their respective houses which are 72 km apart. Rita walked at the rate of 4 kmph while Mona covered 2 km in first hour, 2.5 km in second hour, 3 km is third hour and so on. If they reached the fast food joint at the same time, find the distance of fast food joint from Rita`s house.

  1. 30 km

  2. 36 km

  3. 45 km

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

Mona's distance is an arithmetic progression: 2, 2.5, 3... The sum of n terms is (n/2)(2*2 + (n-1)*0.5). Rita's distance is 4*n. Total distance is 72 km. Solving (n/2)(4 + 0.5n - 0.5) + 4n = 72 leads to 0.25n^2 + 5.75n - 72 = 0. Multiplying by 4 gives n^2 + 23n - 288 = 0. Factoring gives (n+32)(n-9)=0, so n=9. Rita's distance is 4 * 9 = 36 km.

Multiple choice

Two trains leave from the stations Ludhiana and Jalandhar and are both travelling on the same route. Train 1 takes 4 hours to reach Jalandhar, while train 2 takes 9 hours to reach Ludhiana. If train 2 is running at the speed of 48 km/hr, then calculate the speed of train 1.

  1. 148 km/hr

  2. 128 km/hr

  3. 108 km/hr

  4. 118 km/hr

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

The distance between the stations is constant. Let D be the distance. Speed of train 2 = D/9 = 48 km/hr, so D = 432 km. Speed of train 1 = D/4 = 432/4 = 108 km/hr.

Multiple choice

There are two trains moving in opposite directions with the same speed of 50 km/hr and are 100 kms apart at the point of start. There is a bird which flies from one train to the other and repeats the same process as soon as it reaches the other at the speed of 100 km/hr. Calculate the distance travelled by the bird when the trains meet each other.

  1. 75 km

  2. 100 km

  3. 120 km

  4. 150 km

  5. 200 km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The trains are 100 km apart and move toward each other at 50 km/hr each. Relative speed is 100 km/hr, so they meet in 1 hour. The bird flies at 100 km/hr for that entire hour, covering 100 km.

Multiple choice

R and S start at the same time from a place A towards a place B, at a distance of 15 km, at the speeds of 4 km/hr and 6 km/hr, respectively. S reaches B, returns immediately and meets R at C. Find the distance between A and C.

  1. 7.5 km

  2. 18 km

  3. 12 km

  4. 20 km

  5. 15 km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

S travels 15km to B and then some distance back to C. R travels from A to C. Let distance AC = x. S travels 15 + (15 - x) = 30 - x. R travels x. Time is the same: (30-x)/6 = x/4. 120 - 4x = 6x => 10x = 120 => x = 12.

Multiple choice

If Anuj walks at the rate of 5 kmph, he misses the train by 6 minutes. However, if he walks at the rate of 6 kmph, he reaches the station 6 minutes before the arrival of the train. Find the distance covered by him to reach the station.

  1. 8 km

  2. 5 km

  3. 6 km

  4. 7 km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance be D. Time taken at 5 kmph is D/5, and at 6 kmph is D/6. The difference in time is 12 minutes (6 minutes late + 6 minutes early = 12 minutes = 0.2 hours). D/5 - D/6 = 0.2. Solving gives D/30 = 0.2, so D = 6 km.

Multiple choice

Train A left Centerville Station, heading towards Dale City Station, at 3 PM. Train B left Dale City Station, heading toward Centerville Station, at 3:20 PM on the same day. The trains rode on straight tracks that were parallel to each other. If train A travelled at a constant speed of 30 miles per hour and train B travelled at a constant speed of 10 miles per hour, and the distance between Centerville Station and Dale City Station is 90 miles, when did the trains meet each other?

  1. 5:20 pm

  2. 7:20 pm

  3. 5 pm

  4. 7 pm

  5. 9 pm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Train A starts at 3 PM, speed 30 mph. Train B starts at 3:20 PM, speed 10 mph. By 3:20 PM, Train A has traveled 30 * (20/60) = 10 miles. Remaining distance = 90 - 10 = 80 miles. Relative speed = 30 + 10 = 40 mph. Time to meet = 80 / 40 = 2 hours after 3:20 PM, which is 5:20 PM.