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

The speed of the boat in still water is 18 km/hr and the speed of the current is 2 km/hr. If a man rows his boat upstream for 3 hours and downstream for 2 hours. Find the total distance travelled by him?

  1. 94 km

  2. 78 km

  3. 84 km

  4. 88 km
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Upstream speed = 18 - 2 = 16 km/h. Downstream speed = 18 + 2 = 20 km/h. Distance upstream = 16 × 3 = 48 km. Distance downstream = 20 × 2 = 40 km. Total distance = 48 + 40 = 88 km.

Multiple choice

Subham gets on the lift at the 11th floor of a building and rides up at speed of 57 floors per minute. At the same time, Sonali gets on a lift at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross?

  1. 45

  2. 36

  3. 52

  4. 30
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

They start 40 floors apart (51-11) and close the gap at combined speed 120 floors/min. Time to meet is 40/120 = 1/3 min. Subham travels 57×1/3 = 19 floors up from floor 11, reaching floor 30. Option A (45) is above both starting positions. Option B (36) and C (52) ignore the relative motion.

Multiple choice

A train going at 90 km/hr takes 35 minutes to travel a certain distance. By how much should it increase its speed (in km/hr) to travel the same distance in 21 minutes?

  1. 60

  2. 150

  3. 120

  4. 90
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Distance = Speed × Time = 90 × (35/60) = 52.5 km. To cover 52.5 km in 21 minutes, needed speed = 52.5 / (21/60) = 52.5 × 60/21 = 150 km/hr. Increase needed = 150 - 90 = 60 km/hr. Use consistent units (convert minutes to hours) and relate distance = speed × time.

Multiple choice

Sangram goes to his office by car at the speed of 40 Km/h and reaches 30 minute earlier. If he goes at the speed of 30 Km/h, he reaches 30 minutes late. What will be the speed (in Km/hr) of the car to reach on time?
  1. $\(\frac{120}{7}\)$
  2. $\(\frac{240}{7}\)$
  3. $\(\frac{360}{7}\)$
  4. $\(\frac{60}{7}\)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let distance be D km and on-time speed be S km/h. At 40 km/h, reaches 30 min early: D/40 = T - 0.5. At 30 km/h, reaches 30 min late: D/30 = T + 0.5. Subtracting gives D/30 - D/40 = 1, so D(1/30 - 1/40) = 1, D(4/120 - 3/120) = 1, D(1/120) = 1, so D = 120 km. Then T = 120/40 + 0.5 = 3.5 hours. Speed to be on time = 120/3.5 = 240/7 ≈ 34.29 km/h.

Multiple choice

What is the distance between A and B? Statements: I. Two persons Aman and Sangram started simultaneously from A to B with their speed in ratio 4:5. II. Sangram reached B one hour earlier than Aman. III. Difference between speed of Aman and Sangram is 60 km/hr.

  1. Only I and II

  2. Only II and III

  3. All I, II and III

  4. Cannot be answered even including all three statements

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

Let speeds be 4x and 5x km/hr. From III: 5x - 4x = 60, so x = 60. Speeds: 240 km/hr, 300 km/hr. From II: Time difference = 1 hr. If distance = D, then D/240 - D/300 = 1. D(1/240 - 1/300) = 1. D(60/72000) = 1, so D = 1200 km. All three statements are needed. Statement II and III alone don't give initial speed ratio. Statement I and II alone give relationship but not actual values.

Multiple choice

Given that the length of the paths of a ball thrown with different speeds by two boys are the same, if they take 0.6 seconds and 1 seconds respectively to cover the said length, what is the average speed of travel for the first throw, if the same for the second is 96 km/hr?

  1. 100 km/h

  2. 150 km/h

  3. 160 km/h

  4. 200 km/h
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Distance = Speed × Time. Since distances are equal: S₁ × 0.6 = S₂ × 1. Given S₂ = 96 km/hr, S₁ × 0.6 = 96 × 1 = 96, so S₁ = 96/0.6 = 160 km/hr. Option A (100) incorrectly adds 40% to 96. Option B (150) uses 96 × 1.5625 incorrectly. Option D (200) mistakenly uses 96 × 2. This tests the inverse relationship between speed and time for constant distance.

Multiple choice

Two trains are travelling towards each other. The distance between the trains initially is 400 km. After some time they meet at a distance of 150 km from one end. Find the ratio of the speed of the trains.

  1. 2: 5

  2. 3: 5

  3. 4: 7

  4. 7: 3

  5. 3: 7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When trains travel toward each other, they travel for the same time until meeting. One train covers 150 km, the other covers 400 - 150 = 250 km. Since time is constant, the ratio of speeds equals the ratio of distances: 150:250 = 3:5. The slower train traveled 150 km and the faster traveled 250 km.

Multiple choice

Upstream speed is 6 km/hr less than the downstream speed. The speed of the boat is 21 km/hr. Find the time (in hour) to cover the distance of 108 km in the upstream.

  1. 4

  2. 5

  3. 8

  4. 9

  5. 6
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let boat speed = b, stream speed = s. Downstream speed = b + s, Upstream speed = b - s. Given: b - s = (b + s) - 6, so b - s = b + s - 6, giving 2s = 6, so s = 3 km/hr. Boat speed b = 21 km/hr. Upstream speed = 21 - 3 = 18 km/hr. Time for 108 km upstream = 108/18 = 6 hours. Option E is correct.

Multiple choice

A boat takes 3 hours to travel from P to Q against the stream and Q to P along the stream. The distance between Q to P is 4 km. The speed of the stream is 1 km per hour. Find the speed of the boat in still water?

  1. 2

  2. 3

  3. 4

  4. 5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let v be the boat's speed in still water. Downstream speed is v+1 km/h and upstream speed is v-1 km/h. The total time equation is 4/(v+1) + 4/(v-1) = 3 hours. Solving gives 8v = 3(v²-1), which yields v = 3 km/h. The negative solution is rejected as speed cannot be negative.

Multiple choice

Rohit and Mohit start walking from A to B at the same time. After arriving at B, they immediately return to A and they first meet at a distance of 15 km from B. If the difference of their speed is 60 km / h, then find the speed of the faster person? If A and B are 60 km apart.

  1. 120

  2. 180

  3. 175

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

Distance AB = 60 km. They first meet 15 km from B, meaning the faster person covers 60 + 15 = 75 km while the slower covers 60 - 15 = 45 km in the same time. Their speed ratio is 75:45 = 5:3. Let speeds be 5x and 3x. Difference is 2x = 60, so x = 30. Faster speed = 5 × 30 = 150 km/h. This is a standard relative speed problem with return journey.