# Time and Distance Questions and Answers updated daily – Aptitude

Time and Distance Questions: Solved 288 Time and Distance Questions and answers section with explanation for various online exam preparation, various interviews, Aptitude Category online test. Category Questions section with detailed description, explanation will help you to master the topic.

## Time and Distance Questions

41. Without stoppages, a train travels a certain distance with an average speed of 90 km/h, and with stoppages, it covers the same distance with an average speed of 60 km/h. How many minutes per hour the train stops?

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Correct Ans:20

Explanation:

Given without stoppage

Average speed = 90 km/h

With stoppages

Average speed = 60 km/h

We know that,

Time of rest per hour is defined as,

Therefore T = ((90-60)/90)

= (1/3) hr

= (1/3)*60 min

= 20 min

Hence, train stops on an average 20 min per hour.

Average speed = 90 km/h

With stoppages

Average speed = 60 km/h

We know that,

Time of rest per hour is defined as,

**Time of rest per hour = difference in average speed /speed without stoppage.**Therefore T = ((90-60)/90)

= (1/3) hr

= (1/3)*60 min

= 20 min

Hence, train stops on an average 20 min per hour.

Workspace

42. John travelled from his town to city. John went to city by bicycle at the speed of 28 km/h and came back at the speed of 5 km/h. If John took 4 hours and 24 min to complete his journey, what is the distance between town and city?

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Correct Ans:None of these

Explanation:

When the man covers certain distance by x km/hr and comes back at speed of y km/hr then Average Speed = (2xy / (x + y)) km/hr.

Here the

= (2×28×5) / (28 + 5) = 280/33 km/h.

On converting 4 hrs 24 min = 4*(24/60) = 8/5 hrs.

= (280/33) × (8/5) = 13.57 km

Distance between city and town = 13.57/2 km = 6.78 km

Here the

**Average speed**of John =**2xy/(x + y)**= (2×28×5) / (28 + 5) = 280/33 km/h.

On converting 4 hrs 24 min = 4*(24/60) = 8/5 hrs.

**Distance travelled = Speed × Time**= (280/33) × (8/5) = 13.57 km

Distance between city and town = 13.57/2 km = 6.78 km

Workspace

43. The fare of a bus is Rs x for the first five kilometers and Rs 13 per kilometre thereafter. If a passenger pays Rs 2,402/- for a journey of 187 kilometres, what is the value of x?

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Correct Ans:Rs 36/-

Explanation:

Given, Total distance = 187 km

Total bus fare = Rs 2,402/-

Bus fare for first 5 km = Rs. x

Remaining distance = 187 - 5 = 182 km

Bus fare for Remaining distance = Rs. 13 per kilometre

Therefore, Total fare of bus = fare for first 5 km + fare for remaining distance ie., 182 km

----> 2402 = x + [13 * 182]

----> 2402 = x + 2366

----> x = 2402 - 2366

---->

Thus, the

Total bus fare = Rs 2,402/-

Bus fare for first 5 km = Rs. x

Remaining distance = 187 - 5 = 182 km

Bus fare for Remaining distance = Rs. 13 per kilometre

Therefore, Total fare of bus = fare for first 5 km + fare for remaining distance ie., 182 km

----> 2402 = x + [13 * 182]

----> 2402 = x + 2366

----> x = 2402 - 2366

---->

**x = 36**Thus, the

**value of x ie., Bus fare for first 5 km = Rs. 36/-**.
Workspace

44. Two boats A and B start towards each other from two places, 108 km apart. Speeds of the boats A and B in still water are 12 kmph and 15 kmph respectively. If A proceeds downstream and B upstream, they will meet after.

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Correct Ans:4 hours

Explanation:

Let the speed of the stream be x kmph and both the boats meet after t hours

Given, Speed of boat A = 12 kmph

Speed of boat B = 15 kmph

Distance between two boats = 108 km

Boat A proceeds downstream and B upstream.

According to the question,

---> [(12 + x) * t] + [(15 - x) * t] = 108

----> 12t + xt + 15t - xt = 108

----> 27t = 108

---->

Thus, both the boats meet after

Given, Speed of boat A = 12 kmph

Speed of boat B = 15 kmph

Distance between two boats = 108 km

Boat A proceeds downstream and B upstream.

According to the question,

**[Speed downstream * time] + [Speed upstream * time] = Distance between two boats**

Speed upstream = (Speed of boat B - speed of the stream) km/hr.__Formula:-__Speed downstream = (Speed of boat A + speed of the stream) km/hr.Speed upstream = (Speed of boat B - speed of the stream) km/hr.

---> [(12 + x) * t] + [(15 - x) * t] = 108

----> 12t + xt + 15t - xt = 108

----> 27t = 108

---->

**t = 4**Thus, both the boats meet after

**4 hours**.
Workspace

45. The distance between two towns A and B is 545 km. A train starts from town A at 8 A.M. and travels towards town B at 80 km/hr. Another train starts from town B at 9:30 A.M. and travels towards town A at 90 km/hr. At what time will they meet each other?

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Correct Ans:12:00 PM

Explanation:

Given, distance between two towns A and B = 545 km

At 8 A.M., Train 1 starts from town A towards town B with the speed of 80 km/hr.

---> Distance travelled by Train 1 in One and half hours (i.e, from 8:00 AM to 9:30 AM) = Speed * Time = 80 * [1* (1/2)]

= 80 * [3/2]

= 120 km

At 9 : 30 A.M., Train 2 starts from town B towards town A, then

= 545 - 120

=

Now,

(when both trains travelling in opposite direction, we can add the speed).

So,

= 425 / 170

=

So after 9:30 AM two trains meet after 2.5 hrs, ie.,

At 8 A.M., Train 1 starts from town A towards town B with the speed of 80 km/hr.

---> Distance travelled by Train 1 in One and half hours (i.e, from 8:00 AM to 9:30 AM) = Speed * Time = 80 * [1* (1/2)]

= 80 * [3/2]

= 120 km

At 9 : 30 A.M., Train 2 starts from town B towards town A, then

**distance between both trains**= Total Distance - Distance travelled by Train 1 till 9:30 AM= 545 - 120

=

**425 km**Now,

**Relative speed**= 80 + 90 =**170 km/hr**(when both trains travelling in opposite direction, we can add the speed).

So,

**Time when two trains meet each other**= distance between both trains / Relative speed= 425 / 170

=

**2.5 hr**So after 9:30 AM two trains meet after 2.5 hrs, ie.,

**12 Noon.**
Workspace

46. Harish can row a certain distance upstream in 18 hours and downstream the same distance in 12 hours. If the stream flows at the rate of 6 kmph, then find the speed of Harish in still water.

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Correct Ans:30 kmph

Explanation:

Given, upstream time = 18 hours

downstream time = 12 hours

Speed of stream = 6 kmph

Let, Speed of Harish in still water = v kmph

From the given data, it is clear that,

---> Now,

= (speed of Harish in still water - speed of the stream) * time upstream

=

Now,

= (speed of Harish in still water + speed of the stream) * time downstream

=

Then, upstream distance = downstream distance

---> (v - 6) * 18 = (v + 6) * 12

---> (v - 6) * 3 = (v + 6) * 2

---> 3v - 18 = 2v + 12

---> 3v - 2v = 12 + 18

--->

Thus,

downstream time = 12 hours

Speed of stream = 6 kmph

Let, Speed of Harish in still water = v kmph

From the given data, it is clear that,

**upstream distance = downstream distance**---> Now,

**upstream distance**= Speed upstream * time upstream= (speed of Harish in still water - speed of the stream) * time upstream

=

**(v - 6) * 18**Now,

**downstream distance**= Speed downstream * time downstream= (speed of Harish in still water + speed of the stream) * time downstream

=

**(v + 6) * 12**Then, upstream distance = downstream distance

---> (v - 6) * 18 = (v + 6) * 12

---> (v - 6) * 3 = (v + 6) * 2

---> 3v - 18 = 2v + 12

---> 3v - 2v = 12 + 18

--->

**v = 30**Thus,

**Speed of Harish in still water = v = 30 kmph**
Workspace

47. Two persons start running simultaneously around a rectangular track of length 700 m from the same point at speeds of 45 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?

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Correct Ans:36 sec

Explanation:

Given, Length of rectangular track = 700 m

speed of two persons = 45 km/hr and 25 km/hr

---> Since, the persons are running in the opposite direction, the speeds can be added.

thus, Relative speed = Speed of person 1 + Speed of person 2

= 45 + 25

= 70 km/hr

---> Convert km/hr into m/sec

= 700 / [70 * (5/18)]

= (700 * 18) / (70 * 5)

= 2 * 18

=

speed of two persons = 45 km/hr and 25 km/hr

---> Since, the persons are running in the opposite direction, the speeds can be added.

thus, Relative speed = Speed of person 1 + Speed of person 2

= 45 + 25

= 70 km/hr

---> Convert km/hr into m/sec

**Relative speed = 70 * (5/18) m/sec****Time taken by the persons to meet for the first time = Length of the track / relative speed**= 700 / [70 * (5/18)]

= (700 * 18) / (70 * 5)

= 2 * 18

=

**36 sec**
Workspace

48. A truck starts running at the speed of 48 km/hr. If the speed of the truck increases 6 km at the end of every hour then what will be the distance covered at the end of 12 hrs from the start of the Journey?

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Correct Ans:972 km

Explanation:

Given, speed of truck = 48 km/hr

W.K.T:-

Here, Initial Distance covered by truck = 48 km in Time = 1 Hour

At the end of every hour, speed of the truck increases 6 km, ie., Distance increased by 6 km per hour.

So, The total distance covered by the truck at the end of 12 hrs = 48 + 54 + 60 + 66 + 72 + 78 + 84 + 90 + 96 + 102 + 108 + 114

Sum of 12 terms in AP whose first term is 48 and last term is 114

=

Where, n = number of terms = 12

a = first term = 48

l = last term = 114

Thus,

= 6 (162)

=

W.K.T:-

**Speed = Distance/Time**Here, Initial Distance covered by truck = 48 km in Time = 1 Hour

At the end of every hour, speed of the truck increases 6 km, ie., Distance increased by 6 km per hour.

So, The total distance covered by the truck at the end of 12 hrs = 48 + 54 + 60 + 66 + 72 + 78 + 84 + 90 + 96 + 102 + 108 + 114

**By using Arithmetic progression (AP) formula:**Sum of 12 terms in AP whose first term is 48 and last term is 114

=

**S**_{n}= n/2 (a + l)Where, n = number of terms = 12

a = first term = 48

l = last term = 114

Thus,

**The total distance covered by the truck at the end of 12 hrs**= 12/2 ( 48 + 114)= 6 (162)

=

**972 km**
Workspace

49. A boat can travel 55 km downstream in 66 min. The ratio of the speed of the boat in still water to the speed of the stream is 4: 1. How much time will the boat take to cover 84 km upstream?

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Correct Ans:2 hour 48 min

Explanation:

Given, Downstream distance (D) = 55 km

Downstream Time (T) = 66 min

---> converting time in minutes to hour

---> Downstream Time (T) = (66/60) hour

W.K.T:

Given, Speed of the boat in still water : Speed of the stream = 4: 1

---> Speed of the boat in still water = 4x

---> Speed of the stream = x

W.K.T:

---> Speed Downstream = 4x + x = 50

---> 5x = 50

---> x = 10

Thus, Speed of the boat in still water = 4x = 4 * 10 = 40 km/hr

and, Speed of the stream = x = 10 km/hr

Now,

--->

Given, Upstream distance = 84 km

= 84/30

= 2 (4/5) hr

= 2 hour [(4/5) * 60 mins]

=

Downstream Time (T) = 66 min

---> converting time in minutes to hour

---> Downstream Time (T) = (66/60) hour

W.K.T:

**Speed = Distance/Time****Speed Downstream**= (55/66) * 60 =**50 km/hr**Given, Speed of the boat in still water : Speed of the stream = 4: 1

---> Speed of the boat in still water = 4x

---> Speed of the stream = x

W.K.T:

**Speed Downstream = (Speed of the boat in still water + Speed of stream)**---> Speed Downstream = 4x + x = 50

---> 5x = 50

---> x = 10

Thus, Speed of the boat in still water = 4x = 4 * 10 = 40 km/hr

and, Speed of the stream = x = 10 km/hr

Now,

**Speed upstream = (Speed of the boat in still water - Speed of the stream)**--->

**Speed upstream**= 40 - 10 =**30 km/hr**Given, Upstream distance = 84 km

**Time taken by the boat to cover upstream distance**= Upstream distance/ Speed upstream= 84/30

= 2 (4/5) hr

= 2 hour [(4/5) * 60 mins]

=

**2 hour 48 mins**
Workspace

50. A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?

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Correct Ans:100 meter

Explanation:

Relative speed of the thief and policeman = (11 - 10) km/hr = 1 km/hr

Now the relative

= 1 km/hr * 6 mins

(Converting minutes into hour)

= 1 km/hr * (6/60) hr

= 1/10 km

(Converting kilometer into meter)

= 1000/10 meter

=

So,

Now the relative

**distance covered by policeman in 6 min**= Relative Speed * Time= 1 km/hr * 6 mins

(Converting minutes into hour)

= 1 km/hr * (6/60) hr

= 1/10 km

(Converting kilometer into meter)

= 1000/10 meter

=

**100 m**So,

**The distance between policeman and thief after 6 min**= 200 - 100 =**100 m.**
Workspace

51. The respective ratio between the speed of the boat upstream and speed of the boat downstream is 4: 9. What is the speed of the boat in still water if it covers 84 km downstream in 2 hours 20 minutes? (in km/h)

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Correct Ans:26

Explanation:

Given downstream distance = 84 km

downstream time = 2 hours 20 minutes

(Convert 20 minutes to hours)

= 2 hrs + (20/60) hrs

= 2 + (1/3) hrs

= 7/3 hrs

= 84/ (7/3)

= (84 * 3) / 7

= 252/7

=

Given upstream speed : downstream speed = 4 : 9

---> upstream speed = 4x

downstream speed = 9x

Thus, downstream speed = 9x = 36

---> x = 4

Hence,

Now,

= [36 + 16] / 2

= 52/2

=

downstream time = 2 hours 20 minutes

(Convert 20 minutes to hours)

= 2 hrs + (20/60) hrs

= 2 + (1/3) hrs

= 7/3 hrs

**Speed of boat in downstream**= Distance/ Time= 84/ (7/3)

= (84 * 3) / 7

= 252/7

=

**36 km/hr**Given upstream speed : downstream speed = 4 : 9

---> upstream speed = 4x

downstream speed = 9x

Thus, downstream speed = 9x = 36

---> x = 4

Hence,

**upstream speed**(i.e, Speed of boat in upstream) = 4x = 4 * 4 =**16 km/hr**Now,

**Speed of boat in still water = [Speed of boat in downstream + Speed of boat in upstream] / 2**= [36 + 16] / 2

= 52/2

=

**26 km/hr**
Workspace

52. Two trains start at the same time from station A and station B and proceed towards each other at the rate of 16 km and 21 km per hour, respectively. When they meet, it is found that one train has travelled 60 km more than the other. The distance between the two stations is

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Correct Ans:444 km

Explanation:

Since the trains are moving towards each other, their

W.K.T:-

Also, in this case, both the trains travel for the same period of time; hence, when T is constant, D is directly proportional to S.

Hence, Speed of train 1/Speed of train 2 = Distance covered by train 1/Distance covered by train 2

(S1/S2) = 16/21 = (D1/D2)

Let D1 = 16k and D2 = 21k.

Given that one train travelled 60 km more than the other. Train with faster speed covers more distance than slower train.

Hence, 21k - 16k = 60

---> 5k = 60

---> k = 12.

= (16k + 21k)

= 37k

= 37 * 12

=

**relative speed = (16 + 21) = 37**kmph.W.K.T:-

**Speed = Distance/Time**Also, in this case, both the trains travel for the same period of time; hence, when T is constant, D is directly proportional to S.

Hence, Speed of train 1/Speed of train 2 = Distance covered by train 1/Distance covered by train 2

(S1/S2) = 16/21 = (D1/D2)

Let D1 = 16k and D2 = 21k.

Given that one train travelled 60 km more than the other. Train with faster speed covers more distance than slower train.

Hence, 21k - 16k = 60

---> 5k = 60

---> k = 12.

**Total distance between the two stations**is nothing but the distances travelled by the respective trains till the meeting point i.e. (D1 + D2)= (16k + 21k)

= 37k

= 37 * 12

=

**444 km.**
Workspace

53. A man can swim 3 km/hr in still water. If the velocity of the stream is 2 km/hr, the time taken by him to swim to a place 10 km upstream and back is:

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Correct Ans:12 hr

Explanation:

Man = 3 km/hr

Stream = 2 km/hr

Downstream = man + stream = 5 km/hr

Upstream = man - stream = 1 km/hr

Time taken for upstream = 10/1 = 10 hrs

Time taken for downstream = 10/5 = 2 hrs

Total time taken = 12 hrs

Stream = 2 km/hr

Downstream = man + stream = 5 km/hr

Upstream = man - stream = 1 km/hr

Time taken for upstream = 10/1 = 10 hrs

Time taken for downstream = 10/5 = 2 hrs

Total time taken = 12 hrs

Workspace

54. A Man travelled a distance of 61 km in 9 hours. He travelled partly on foot at 4 km/hr and partly on bicycle at 9 km/hr. What is the distance travelled on foot?

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Correct Ans:16 km

Explanation:

Let the time in which he travelled on foot = x hour

Time for travelling on bicycle = (9 - x) hr

Distance = Speed * Time

Distance travelled by foot = 4x km

Distance travelled by bicycle = 9(9 - x) km

Total distance = 61 km

So,4x + 9(9-x) = 61

=> 5x = 20

=> x = 4

So distance traveled on foot = 4(4) = 16 km

Time for travelling on bicycle = (9 - x) hr

Distance = Speed * Time

Distance travelled by foot = 4x km

Distance travelled by bicycle = 9(9 - x) km

Total distance = 61 km

So,4x + 9(9-x) = 61

=> 5x = 20

=> x = 4

So distance traveled on foot = 4(4) = 16 km

Workspace

55. A man rows 750 m in 675 seconds against the stream and returns in 7 and half minutes. His rowing speed in still water is

SHOW ANSWER

Correct Ans:5 km/hr

Explanation:

Upstream = (750/675) = 10/9 m/sec

Downstream = (750/450) = 5/3 m/sec

Still water = (1/2)*[(10/9) + (5/3)] m/sec.

= 25/18 m/sec

= (25/18)*(18/5) kmph

= 5 kmph

Downstream = (750/450) = 5/3 m/sec

Still water = (1/2)*[(10/9) + (5/3)] m/sec.

= 25/18 m/sec

= (25/18)*(18/5) kmph

= 5 kmph

Workspace

56. A salesman travels a distance of 50 km in 2 hours and 30 minutes. How much faster, in kilometers per hour, on an average, must he travel to make such a trip in 5/6 hour less time?

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Correct Ans:10

Explanation:

Given that,

Distance = 50 km

Time = 2 hrs 30 mins = 2(1/2) hrs = 5/2 hrs

Original speed = D/T = 50/(5/2) = 20 km/hr

Required time to make a trip 5/6 hrs less time = 5/2 - 5/6

= 5/3 hrs

Speed = D/T = 50/(5/3) = 30 km/hr

Speed difference = 30 - 20 = 10 km/hr

So, he must travel 10 km/hr speed faster to make a trip 5/6 hour less time.

Distance = 50 km

Time = 2 hrs 30 mins = 2(1/2) hrs = 5/2 hrs

Original speed = D/T = 50/(5/2) = 20 km/hr

Required time to make a trip 5/6 hrs less time = 5/2 - 5/6

= 5/3 hrs

Speed = D/T = 50/(5/3) = 30 km/hr

Speed difference = 30 - 20 = 10 km/hr

So, he must travel 10 km/hr speed faster to make a trip 5/6 hour less time.

Workspace

57. Krish can swim at 20 km/hr in still water. The river flows at 8 km/hr and it takes 8 hours more upstream than downstream for the same distance. How far is the place?

SHOW ANSWER

Correct Ans:168 km

Explanation:

Speed of downstream (20 + 8) = 28 km/hr

Speed of upstream (20-8) = 12 km/hr

According to the question,

[x/12 - x/28] = 8

(7x - 3x) / 84 = 8

4x/84 = 8

x/21 = 8

x= 168 km

Speed of upstream (20-8) = 12 km/hr

According to the question,

[x/12 - x/28] = 8

(7x - 3x) / 84 = 8

4x/84 = 8

x/21 = 8

x= 168 km

Workspace

58. The ratio between the speeds of two trains is 7: 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is ?

SHOW ANSWER

Correct Ans:87.5 km/hr

Explanation:

Let the speeds of two trains be 7X and 8X km/hr.

8X = 400/4

=> X = 12.5Km/hr

So speed of first train is 7*12.5 = 87.5 km/hr

8X = 400/4

=> X = 12.5Km/hr

So speed of first train is 7*12.5 = 87.5 km/hr

Workspace

59. In a voyage of 600 km, a ship was slowed down due to bad weather and storm in Ocean. Its average speed for the trip was reduced by 200 km/hr, and the time of trip increased by 30 minutes. What would be the duration of the voyage?

SHOW ANSWER

Correct Ans:1 hour

Explanation:

Let the duration be x hours.

600/x - 600/(x+1/2) = 200

600/x - 1200/(2x+1) = 200

200(3/x - 6/(2x+1)) = 200

3/x - 6/(2x+1) = 1

3(2x+1) - 6x / x(2x+1) = 1

6x+3-6x / 2x

3 = 2x

2x(x+3) - 2x + 3x - 3 = 0

2x(x-1) + 3(x-1) = 0

x = 1, -3/2

x = 1 hour

600/x - 600/(x+1/2) = 200

600/x - 1200/(2x+1) = 200

200(3/x - 6/(2x+1)) = 200

3/x - 6/(2x+1) = 1

3(2x+1) - 6x / x(2x+1) = 1

6x+3-6x / 2x

^{2}+x = 13 = 2x

^{2}+x2x(x+3) - 2x + 3x - 3 = 0

2x(x-1) + 3(x-1) = 0

x = 1, -3/2

x = 1 hour

Workspace

60. A person has to travel from point B in certain time. Travelling at a speed of 5 kmph he reaches 48 minutes late and while travelling at a speed of 8 kmph he reaches 15 minutes early. What is the distance from point A to point B ?

SHOW ANSWER

Correct Ans:14 km

Explanation:

Let the distance between A and B be x km.

Difference of time = 48+15 = 63 minutes

= 63/60 hours

According to the question,

x/5 - x/8 = 63/60

(8x - 5x)/40 = 63/60

3x/2 = 21

3x = 42

x = 14 km.

Difference of time = 48+15 = 63 minutes

= 63/60 hours

According to the question,

x/5 - x/8 = 63/60

(8x - 5x)/40 = 63/60

3x/2 = 21

3x = 42

x = 14 km.

Workspace

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