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

Abhi finishes a journey by car in 9 hours. He travels the first half of the journey at a speed of 40 km/h and the second half of the journey at a speed of 50 km/h. The total distance covered is:

  1. 350 km

  2. 450 km

  3. 400 km

  4. 300 km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let total distance = 2d km. Time for first half = d/40 hours, second half = d/50 hours. Total time = d/40 + d/50 = d(1/40 + 1/50) = d(5/200 + 4/200) = 9d/200 = 9 hours. Solving: 9d = 1800, d = 200 km. Total distance = 2d = 400 km.

Multiple choice

boat can cover a distance of 7.2 km downstream and 3.2 km upstream in 2 hours. It can also cover 1.5 km downstream and 0.6 km upstream in 24 minutes. What is the speed of the boat when going downstream (in km/h) ? नाव धारा के अनुकूल 7.2 किमी और धारा के प्रतिकूल 3.2 किमी की दूरी 2 घंटे में तय कर सकती है। यह 1.5 किमी अनुकूल और 0.6 किमी प्रतिकूल 24 मिनट में तय कर सकती है। धारा के अनुकूल जाते समय नाव की गति (किमी/घंटा में) क्या है?

  1. 6

  2. 4.5

  3. 5

  4. 7.5

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

Let boat speed in still water be b and stream speed be c. Downstream speed = b + c, upstream = b - c. First condition: 7.2/(b+c) + 3.2/(b-c) = 2 hours. Second condition (24 min = 0.4 hours): 1.5/(b+c) + 0.6/(b-c) = 0.4. Multiply second by 4: 6/(b+c) + 2.4/(b-c) = 1.6. Notice this is close to the first equation. Subtract: (7.2-6)/(b+c) + (3.2-2.4)/(b-c) = 2-1.6, so 1.2/(b+c) + 0.8/(b-c) = 0.4. Multiply by 5: 6/(b+c) + 4/(b-c) = 2. From original second equation (×10): 15/(b+c) + 6/(b-c) = 4. Solve: Let x = 1/(b+c), y = 1/(b-c). We have 15x + 6y = 4 and 6x + 4y = 2. From second: 3x + 2y = 1, so y = (1-3x)/2. Substituting: 15x + 6(1-3x)/2 = 4, so 15x + 3 - 9x = 4, giving 6x = 1, x = 1/6. Therefore b + c = 6 km/h. Option B (4.5) would be if we miscalculated the relationship.

Multiple choice

A boat goes downstream and covers 84 km distance in 12 hours and when it goes upstream, cover half of the downstream distance at the same time. Find the speed of the current.

  1. 7/4 km/hour

  2. 4/7 km/hour

  3. 21/4 km/hour

  4. 4/21 km/hour
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Downstream: Distance = 84 km, Time = 12 hours, so downstream speed = 84/12 = 7 km/h = (b + c) where b is boat speed and c is current speed. Upstream: Distance = 42 km (half of 84), Time = 12 hours, so upstream speed = 42/12 = 3.5 km/h = (b - c). Subtracting: (b + c) - (b - c) = 7 - 3.5, so 2c = 3.5, giving c = 1.75 km/h = 7/4 km/h.

Multiple choice

Hemant travels first 40% of total distance at the speed of 1.25 m/sec and takes rest for 24 minutes. Then he covers remaining distance at the speed of 5/3 m/sec. If he took total 2 hours 40 minutes to complete the journey then find the distance of the journey.

  1. 10 km

  2. 12 km

  3. 15 km

  4. 8 km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total time = 2 hr 40 min = 160 min. Rest = 24 min, so travel time = 136 min. First 40% at 1.25 m/s = 75 m/min, remaining 60% at 5/3 m/s = 100 m/min. Let distance be D. Time = 0.4D/75 + 0.6D/100 = 136. Solving: D(0.4/75 + 0.6/100) = 136, D(0.00533 + 0.006) = 136, D(0.01133) = 136, D = 12000 m = 12 km. Option A is calculation error, C from wrong speed conversion, D from subtracting instead of adding.

Multiple choice

A man can reach a certain place in 40 hours. If he reduces his speed by 1/13th, he goes 5 km less in that time. Find the total distance covered by him?

  1. 45 km

  2. 65 km

  3. 72 km

  4. 55 km

  5. 56 km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let original speed be v km/hr. Distance = v × 40 km. Reduced speed = v - v/13 = 12v/13 km/hr. Distance at reduced speed = (12v/13) × 40 = 480v/13 km. Difference: 40v - 480v/13 = (520v - 480v)/13 = 40v/13 = 5 km. So v = (5 × 13)/40 = 65/40 = 13/8 km/hr. Original distance = (13/8) × 40 = 65 km.

Multiple choice

A boat goes 9 km for an hour in still water. It takes twice as much time for the boat to go upstream as it takes while going downstream. Find the speed of the current?

  1. 2 km/hr

  2. 5 km/hr

  3. 3 km/hr

  4. 8 km/hr

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

Let boat speed in still water = b = 9 km/hr, current speed = c. Downstream speed = b+c, upstream speed = b-c. Time upstream = 2 × time downstream. Distance upstream = distance downstream (let it be d). So d/(b-c) = 2d/(b+c). Cross-multiplying: d(b+c) = 2d(b-c). b+c = 2b-2c. 3c = b. Therefore current speed c = 9/3 = 3 km/hr. This matches option C.

Multiple choice

The distance between two stations A and B is 200 km. A train runs from A to B at a speed of 75 km/hr, while another train runs from B to A at a speed of 85 km/hr. What will be the distance (in km) between the two trains 3 minutes before they meet?

  1. 5

  2. 8

  3. 10

  4. 6
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Relative speed = 75 + 85 = 160 km/hr. In 3 minutes (3/60 = 1/20 hour), distance covered = 160 × 1/20 = 8 km. This is the distance between trains 3 minutes before meeting, regardless of starting distance. The trick is recognizing that the distance covered in 3 minutes IS the gap.

Multiple choice

A man can reach a certain place in 21.75 hours. If he reduces his speed by (\frac{1}{15})th, he goes 10 km less in that time. Find the total distance covered by him.

  1. 140 km

  2. 150 km

  3. 142.5 km

  4. 160 km

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

Let original speed = s km/h. Distance = s × 21.75. Reduced speed = (14/15)s, distance in same time = (14/15)s × 21.75. Difference = s × 21.75 - (14/15)s × 21.75 = s × 21.75 × (1/15) = 10 km. So s × 1.45 = 10, giving s = 50/7. Total distance = (50/7) × 21.75 = 50 × 3.09 = 154.5, which rounds to approximately 150 km.

Multiple choice

When a person increases his speed by 3 km/h, he reaches the office 10 minutes earlier. When he reduces his speed by 4 km/h, he reaches 20 minutes late, then what is his actual speed and what is the distance of his office from home?

  1. 12 km/hr , 126 km

  2. 21 km/hr , 64 km

  3. 18 km/hr , 21 km

  4. 25 km/hr , 125 km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let actual speed be v km/h and distance be d km. When speed increases to (v+3), time saved is 10 minutes: d/(v+3) = d/v - 10/60. When speed decreases to (v-4), time lost is 20 minutes: d/(v-4) = d/v + 20/60. Solving these equations yields v = 18 km/h and d = 21 km, which satisfies both conditions.

Multiple choice

In a journey of three unequal laps, a car covers a distance of 200 km in 4 h in the first lap, while another 162 km at the speed of 15 m/s in the second lap. It covered the remaining distance of the final lap in 4 h such that the average speed of the car for entire journey was 50 km/h. What was the speed of the car in the third lap of the journey?

  1. 47 km/h

  2. 52 km/h

  3. 42 km/h

  4. 45 km/h
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Lap 1: 200 km in 4h = 50 km/h. Lap 2: 162 km at 15 m/s = 54 km/h, time = 162/54 = 3h. Total average = 50 km/h. Total time needed = (total distance)/(avg speed) = (200 + 162 + d3)/50. Let t3 = 4h. Then (362 + d3)/50 = 4 + 3 + 4 = 11h, so d3 = 550 - 362 = 188 km. Speed in lap 3 = 188/4 = 47 km/h. Options B (52), C (42), and D (45) are incorrect.

Multiple choice

A train covers a distance of 225km in 2½ hours at a uniform speed. The time taken by the train (in hours) to cover a distance of 630km at the same speed is:

  1. 6

  2. 7

  3. 4

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

Speed = distance/time = 225/2.5 = 90 km/h. For 630 km at same speed: time = distance/speed = 630/90 = 7 hours. This uniform speed problem requires calculating speed first, then applying it to the new distance. The key is maintaining the same speed throughout.

Multiple choice

Two men start walking from A & B, at a distance of 63 km towards each other at same time. The speed of first person is 4 km/h, while the other one starts at 2 km/h and increases his speed every hour by 1 km/h, then after what duration will they meet?

  1. 7 hours

  2. 9 hours

  3. 5 hours

  4. 6 hours
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

After 7 hours, first person travels 28 km (4 × 7). Second person travels 1+2+3+4+5+6+7 = 35 km (sum of first 7 natural numbers, starting at 2 km/h). Total = 63 km, exactly the initial distance. At 6 hours, they'd only travel 24 + 21 = 45 km, which is less than 63 km.

Multiple choice

In the festival of Onam three boats A, B and C with speeds 17 k/h, 23 k/h and 15 k/h participated for a race of 105 km. If the speed of stream is 3 k/h and the boats are running in the direction of stream then find by what distance winner boat is ahead of the last boat.

  1. 45 km

  2. 44 km

  3. 41 km

  4. 42 km
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Effective speeds in stream direction: A = 17 + 3 = 20 km/h, B = 23 + 3 = 26 km/h, C = 15 + 3 = 18 km/h. Time taken: A = 105/20 = 5.25 hours, B = 105/26 = 4.04 hours (winner), C = 105/18 = 5.83 hours. Distance between winner B and last C when B finishes: Distance by C = 18 × 4.04 = 72.7 km. Lead = 105 - 72.7 ≈ 42 km.

Multiple choice

Two friends A and B are standing at points P and Q respectively. A starts moving from points P towards point Q with speed of (x – 2.5) km/hr. After 2 hours, B starts moving towards point P from point Q with speed of (x + 5) km/hr. and they meet at the midpoint of P and Q. Find the time taken by A to go from point P to point Q, if the distance between point P and point Q is 360 km.

  1. 20 hours

  2. 16 hours

  3. 12 hours

  4. 15 hours

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

Since A and B meet at the midpoint, each travels 180 km. A travels for t hours, B starts 2 hours late so travels (t-2) hours. Equating distances: (x-2.5)t = 180 and (x+5)(t-2) = 180. Solving gives x = 25 and t = 8 hours to reach midpoint. Total time for full 360 km journey = 360/(x-2.5) = 360/22.5 = 16 hours.

Multiple choice

The distance between the places P and Q is D units. The average speed that gets a person from P to Q in a stipulated time is S units. He takes 20 minutes more time than usual if he travels at 60 Km/h, and reaches 44 minutes early if he travels at 75 Km/h. The sum of the thrice the numerical values of D and thrice the numerical value of S is:

  1. 1028

  2. 1088

  3. 384

  4. 1152
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let usual time be t hours, stipulated time. Distance D = S × t. At 60 km/h: time = t + 20/60, so D = 60(t + 1/3) = 60t + 20. At 75 km/h: time = t - 44/60, so D = 75(t - 11/15) = 75t - 55. Equating: 60t + 20 = 75t - 55 → 15t = 75 → t = 5 hours. Then D = S × 5, and also D = 60 × 5 + 20 = 320, so S = 64 km/h. 3D + 3S = 3(320) + 3(64) = 960 + 192 = 1152. The problem involves two scenarios with different speeds and time deviations from stipulated time.