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

Ramesh travels at the rate of 3 km/hr and he reaches 15 min late. If he travels at the rate of 4km/h, he reaches 15 min. earlier. The distance covered by Ramesh is - रमेश 3 किमी/घं. की चाल से चलता है और वह 15 मिनट की देरी से पहुचँता है। यदि वह 4 किमी/घं. की चाल से चले तो 15 मिनट पहले पहुँच जाता है। रमेश द्वारा चली गई दूरी है:

  1. 7.5 km./किमी.

  2. 6 km./किमी.

  3. 5 km./किमी.

  4. 4.5 km,/किमी.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let distance = d km and scheduled time = t hours. At 3 km/hr: d/3 = t + 15/60 (15 minutes late). At 4 km/hr: d/4 = t - 15/60 (15 minutes early). Subtract: d/3 - d/4 = 30/60 = 0.5, so d/12 = 0.5, giving d = 6 km. Option B is correct. The time difference between slow and fast speed is 30 minutes total.

Multiple choice

If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. At which speed he should travel to complete his initial distance in 4 hours? यदि कोई व्यक्ति 10 किमी/घंटा की बजाय 14 किमी / घंटा की गति से चलता है, तो वह 20 किमी अधिक चल सकता है। अपनी प्रारंभिक दूरी को 4 घंटे में पूरा करने के लिए उसे किस गति से यात्रा करनी चाहिए?

  1. 15.5 Km/h किमी/घं

  2. 12.5 Km/h किमी/घं

  3. 14 Km/h किमी/घं

  4. 18 Km/h किमी/घं
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Difference in speed = 4 km/hr, extra distance covered = 20 km. Time taken = 20/4 = 5 hours. Initial distance = 10 × 5 = 50 km. To cover 50 km in 4 hours: Speed = 50/4 = 12.5 km/hr. The time calculated is the time actually walked at both speeds.

Multiple choice

Which information is/are sufficient to answer the questions asked? A boat covers 24 km upstream and 36 km downstream in 6 hours. What is the velocity of current? I. Speed of boat in still water is 10 km/hr. II. Boat covers 36 km upstream and 24 km downstream in 6.5 hours. III. The boat covers 48 km upstream in 6 hours and downstream in 4 hours.

  1. I or II only

  2. II or III only

  3. II and (I or III)

  4. Any one is sufficient

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

For the given data: 24 km upstream + 36 km downstream in 6 hours. Let boat speed = b, current speed = c. We have 24/(b-c) + 36/(b+c) = 6. Statement I: b = 10 km/hr gives 24/(10-c) + 36/(10+c) = 6, which solves to c = 2 km/hr - sufficient alone. Statement II: 36 km upstream + 24 km downstream in 6.5 hours gives a second equation, making two equations in two variables (b, c) - sufficient alone. Statement III: 48 km upstream in 6 hours means b-c = 8 km/hr; 48 km downstream in 4 hours means b+c = 12 km/hr. Solving gives c = 2 km/hr - sufficient alone. Each statement independently determines the current velocity.

Multiple choice

Find the value of both quantities and state the correct relationship. Quantity I: speed of swimmer in still water, if he can swim downstream at 14 km/hr and upstream at 6 km/hr. Quantity II: speed of swimmer in still water, if he swims a distance of 36 km downstream in 6 hours and a distance of 40 km upstream in 8 hours.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: If downstream speed is 14 km/hr and upstream speed is 6 km/hr, then speed of swimmer in still water = (downstream + upstream)/2 = (14 + 6)/2 = 10 km/hr. Quantity II: Downstream distance 36 km in 6 hours gives downstream speed = 6 km/hr. Upstream distance 40 km in 8 hours gives upstream speed = 5 km/hr. Speed in still water = (6 + 5)/2 = 5.5 km/hr. Comparing: 10 > 5.5, so Quantity I > Quantity II.

Multiple choice

A boat goes upstream at a speed of 15 km/hr and comes back the same distance at 24 km/hr. What is the average speed (in km/hr) for the total journey? (Approx) एक नाव एक स्थान पर 15 किमी /घंटा की चाल से उर्ध्वप्रवाह जाती है और 24 किमी/घंटा की अनुप्रवाह चाल से वापस आती है। कुल यात्रा के दौरान औसत गति (किमी/घंटा में) क्या है? (लगभग)

  1. 17.4

  2. 18.5

  3. 19.3

  4. 18.9
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For equal distances at speeds 15 km/hr (upstream) and 24 km/hr (downstream), average speed = 2×15×24/(15+24) = 720/39 = 18.46 km/hr, approximately 18.5 km/hr. This is the harmonic mean of the two speeds.

Multiple choice

Shagun travels 486 km in 5.25 hours in two stages. In the first part of the journey, she travels by bus at the speed of 78 km per hour. In the second part of the journey, she travels by train at the speed of 112 km/hr. How much distance does she travel by train? शगुन दो चरणों में 486 किमी की यात्रा 5.25 घंटों में करती है। यात्रा के पहले भाग में, वह प्रति घंटे 78 किमी की रफ्तार से बस से यात्रा करती है। यात्रा के दूसरे भाग में, वह 112 किमी / घंटा की रफ्तार से ट्रेन से यात्रा करती है। वह ट्रेन से कितनी दूरी यात्रा करती है?

  1. 252 km./किमी.

  2. 256 km./किमी.

  3. 258 km./किमी.

  4. 249 km./किमी.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let distance by bus = x km and by train = y km. Then x + y = 486 and x/78 + y/112 = 5.25. Substituting x = 486 - y into the time equation and solving: (486 - y)/78 + y/112 = 21/4. Multiplying by 34944 and simplifying gives 136y = 34272, so y = 252 km. The claimed answer is correct.

Multiple choice

A bike covers a distance of 36 km at a uniform speed. Had the speed been 6 kmph less, it would have taken one hour more for the journey. The original speed of the bike was एक बाइक एक समान गति से 36 किमी की दूरी को कवर करती है। यदि गति 6 किमी प्रति घंटे कम होती, तो यात्रा के लिए एक घंटे और अधिक समय लगेगा । बाइक की मूल गति थी

  1. 16 kmph/(किमी./घंटा)

  2. 19 kmph/(किमी./घंटा)

  3. 17 kmph/(किमी./घंटा)

  4. 18 kmph/(किमी./घंटा)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let original speed = x kmph. Time taken at x kmph = 36/x hours. At (x-6) kmph, time = 36/(x-6) hours. Difference is 1 hour: 36/(x-6) - 36/x = 1. Solving gives x=18. At 18 kmph, time is 2 hours. At 12 kmph, time is 3 hours - 1 hour more.

Multiple choice

When the speed of a train is increased by 20%, it takes 20 minutes less to cover the same distance. What is the time taken to cover the same distance with the original speed? जब ट्रेन की चाल में 20% की वृद्धि होती है, तो उसी दूरी को तय करने में 20 मिनट कम लगते हैं। मूल चाल के साथ उसी दूरी को तय करने के लिए लिया गया समय क्या है?

  1. 2 hours 20 minutes

  2. 2 hours

  3. 1 hour 40 minutes

  4. 1 hour 20 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let original speed = v, original time = t. New speed = 1.2v. Since distance is same: v×t = 1.2v×(t-20). Dividing by v: t = 1.2(t-20). t = 1.2t - 24. 0.2t = 24. t = 120 minutes = 2 hours. When speed increases by 20%, time becomes 5/6 of original, saving 1/6 of the time.

Multiple choice

(\text{Find the value of quantities and state the correct relationship.}\\text{Quantity I: Speed of boat in still water if it took 24 hours to cover a distance of 64 km going downstream and back. Given the speed of current to be 2 km/hr} \\text{Quantity II: Average speed of a boy to go from home to school if his average speed is 2 km/hr from school to home and he covers a total of 12 km in 5 hours.})

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Let boat speed = b. Downstream (32 km) at b+2, upstream (32 km) at b-2. Total time 24 hours gives 32/(b+2) + 32/(b-2) = 24. Solving yields b = 4 km/hr. Quantity II: Total distance = 12 km in 5 hours gives average speed = 12/5 = 2.4 km/hr. Comparing: 4 > 2.4, so Quantity I > Quantity II.

Multiple choice

Find the speed of the stream. (I) A boat can cover the distance in 5 hr. upstream. (II) It can cover the distance in 3 hr. downstream. (III) It covers the distance of 10 km.

  1. Only II

  2. Only III

  3. I & either II or III

  4. All the three are necessary

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

Let boat speed = b, stream speed = s. Upstream: (b-s) × 5 = distance. Downstream: (b+s) × 3 = distance. Statement III gives distance = 10 km. Setting up: 5(b-s) = 10 and 3(b+s) = 10. This gives b-s = 2 and b+s = 10/3. Solving: 2b = 2 + 10/3 = 16/3, so b = 8/3. Then s = 10/3 - 8/3 = 2/3 km/hr. All three statements are necessary.

Multiple choice

In each of the following questions, a question is followed by two statements numbered I and II. Read both the statements and answer accordingly. Ques. What of the distance travelled? (I) : If a person covers a distance in 12 hour, covering the first half at 20 kmph and the second half at 30 kmph (II) : If a person covers a distance at 30 kmph. If he decreases his speed to 25 kmph he takes two more hour to reach the destination

  1. Only I

  2. Only II

  3. Either I or II

  4. Neither I nor II

  5. Both I and II
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I: Average speed for two equal distances = 2×20×30/(20+30) = 24 kmph. Distance = 24×12 = 288 km. Statement II: Let distance = d, then d/30 - d/25 = 2, which gives d = 300 km. Either statement alone is sufficient.

Multiple choice

A man can row 8 km/hr in still water. If the speed of the current is 4 km/hr, it takes 2 hrs more in upstream than in the downstream for the same distance. Find distance.

  1. 10 km.

  2. 12 km.

  3. 14 km.

  4. 8 km.

  5. 16 km.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Speed in still water = 8 km/h, current speed = 4 km/h. Downstream speed = 8+4 = 12 km/h. Upstream speed = 8-4 = 4 km/h. Let distance = d. Time upstream = d/4, Time downstream = d/12. Given: d/4 - d/12 = 2 hours. Solving: (3d - d)/12 = 2, so 2d/12 = 2, giving 2d = 24, so d = 12 km. Option B is correct.

Multiple choice

While travelling a distance of 48 km, Ballu covers it two hours faster than he had planned to. This he achieved by travelling 1 km more every hour than he intended to cover in every 1 hour 15 minutes. What the speed at which Ballu is travelling ?

  1. 8 km/hr.

  2. 12 km/hr.

  3. 9 km/hr.

  4. 10.5 km/hr.

  5. 7.5 km/hr.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Ballu traveled 48 km 2 hours faster than planned. His actual speed was 1 km/hr more than intended for every 1 hr 15 min. Intended speed per 1.25 hrs = 10 km, so intended speed = 8 km/hr. Planned time = 48/8 = 6 hours. Actual time = 6 - 2 = 4 hours. Actual speed = 48/4 = 12 km/hr.

Multiple choice

The questions given below contain three statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question ? What is the speed of a car ? (I) The speed of the car is 10 km/hr more than the speed of a motorbike. (II) The motorbike takes 2 hours more than the car in order to cover a distance of 400 km. (III) The ratio between the speed of motorbike and car is 4:5 respectively.

  1. All

  2. Only I and II

  3. Only II and III

  4. Any two of them

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

Data sufficiency analysis: Statement I gives car speed as bike speed + 10. Statement II gives 400/B - 400/C = 2. Statement III gives B/C = 4/5. Using I and II: C = B + 10, solving gives B = 40, C = 50. Using I and III: C = B + 10 and B = 0.8C gives B = 40, C = 50. Using II and III also gives C = 50. Thus any two statements together are sufficient.