All questions of Speed, Distance and Time for Delhi Police Constable Exam

Two boys starts from the same place walking at the rate of 5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 8.5 km apart?
  • a)
    17 hr
  • b)
    14 hr
  • c)
    12 hr
  • d)
    19 hr
Correct answer is option 'A'. Can you explain this answer?

In this type of questions we need to get the relative speed between them, 
The relative speed of the boys = 5.5kmph – 5kmph
= 0.5 kmph
Distance between them is 8.5 km
Time = Distance/Speed
Time= 8.5km / 0.5 kmph = 17 hrs

If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. What is the actual distance travelled by him?
  • a)
    80 km
  • b)
    70 km
  • c)
    60 km
  • d)
    50 km
Correct answer is option 'D'. Can you explain this answer?

Distance he could travelled/speed diff.
= 20/(14-10)
= 20/4
= 5 hrs
Now his actual speed was 10 km/h
Total distance travelled by him = speed × time
= 10 × 5
= 50 km.
 

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?
  • a)
    12km
  • b)
    14km
  • c)
    16km
  • d)
    18km
Correct answer is option 'C'. Can you explain this answer?

EduRev CAT answered
Let the time in which he travelled on foot = x hour
Time for travelling on bicycle = (9 - x) hr

Distance = Speed * Time, and Total distance = 61 km
So,
4x + 9(9-x) = 61
=> 5x = 20
=> x = 4

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

A train of 300 m is travelling with the speed of 45 km/h when it passes point A completely. At the same time, a motorbike starts from point A with the speed of 70 km/h. When it exactly reaches the middle point of the train, the train increases its speed to 60 km/h and motorbike reduces its speed to 65 km/h. How much distance will the motorbike travel while passing the train completely?
  • a)
    2.52 km
  • b)
    2.37 km
  • c)
    2 km
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Shalini Bajaj answered
Speed of train while passing point
A = 70 x (5/18) m/s = VI
Speed of bike initially = 70 x (5/18) m/s = V2
Time taken by the bike to reach at the mid-point of the train = 1 5 0 /(V 2 - V I)
Again find out the new speeds of train and bike, and calculate the time taken by the bike to cover the rest 150 m distance relative to the train.

A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.?
  • a)
    5
  • b)
    6
  • c)
    7
  • d)
    8
Correct answer is option 'C'. Can you explain this answer?

Relative speed = Speed of A + Speed of B (∴ they walk in opposite directions)
=2+3 = 5 rounds per hour
Therefore, they cross each other 5 times in 1 hour and 2 times in 1/2 hour
Time duration from 8 a.m. to 9.30 a.m. = 1.5 hour
Hence they cross each other 7 times before 9.30 a.m.

A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
  • a)
    121 km
  • b)
    242 km
  • c)
    224 km
  • d)
    112 km
Correct answer is option 'C'. Can you explain this answer?

Dhruv Mehra answered
Let time taken to travel the first half = x hr 
Then time taken to travel the second half = (10 - x) hr 

Distance covered in the the first half = 21x [because, distance = time*speed]
Distance covered in the the second half = 24(10 - x)

Distance covered in the the first half = Distance covered in the the second half
So,
21x = 24(10 - x)
=> 45x = 240
=> x = 16/3
Total Distance = 2*21(16/3) = 224 Km [multiplied by 2 as 21x was distance of half way]

Practice Quiz or MCQ (Multiple Choice Questions) with solution are available for Practice, which would help you prepare for Time & Distance under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.
 
Q. A man takes 5 hours 45 min in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways is
  • a)
    11 hrs
  • b)
    8 hrs 45 min
  • c)
    7 hrs 45 min
  • d)
    9 hrs 20 min
Correct answer is option 'C'. Can you explain this answer?

Manoj Ghosh answered
Given that time taken for riding both ways will be 2 hours lesser than
the time needed for waking one way and riding back
From this, we can understand that
time needed for riding one way = time needed for waking one way - 2 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min
In fact, you can do all these calculations mentally and save a lot of time
which will be a real benefit for you.

The Sinhagad Express left Pune at noon sharp. Two hours later, the Deccan Queen started from Pune in the same direction. The Deccan Queen overtook the Sinhagad Express at 8 p.m. Find the average speed of the two trains over this journey if the sum of their average speeds is 70 km/h.
  • a)
    34.28 km/h
  • b)
    35 km/h
  • c)
    50 km/h
  • d)
    12 km/h
Correct answer is option 'A'. Can you explain this answer?

Ishani Rane answered
The ratio of time for the travel is 4:3 (Sinhagad to Deccan Queen). Hence, the ratio of speeds
would be 3:4. Since, the sum of their average speeds is 70 kmph, their respective speeds would
be 30 and 40 kmph respectively. Use alligation to get the answer as 34.28 kmph.

Ram and Bharat travel the same distance at the rate of 6 km per hour and 10 km per hourrespectively. If Ram takes 30 minutes longer than Bharat, the distance travelled by each is
  • a)
    6 km
  • b)
    10 km
  • c)
    7.5 km
  • d)
    20 km
Correct answer is option 'C'. Can you explain this answer?

Aarav Sharma answered
Given information:
- Ram's speed = 6 km/h
- Bharat's speed = 10 km/h
- Ram takes 30 minutes longer than Bharat

To find:
- Distance travelled by each

Solution:
Let's assume the distance travelled by both Ram and Bharat is 'd' km.

Time taken by Ram = Distance/Speed = d/6 hours
Time taken by Bharat = Distance/Speed = d/10 hours

As per the given information, Ram takes 30 minutes longer than Bharat. We know that 30 minutes is equal to 0.5 hours. So,

d/6 = d/10 + 0.5

Now, let's solve for 'd'.

d/6 - d/10 = 0.5

(10d - 6d)/60 = 0.5

4d = 30

d = 7.5 km

Therefore, the distance travelled by each is:
- Ram = d/6 = 7.5/6 = 1.25 hours
- Bharat = d/10 = 7.5/10 = 0.75 hours

Hence, the correct answer is option 'C'.

There are two swimmers A and B who start swimming towards each other from opposite banks of the lake. They meet at a point 900 ft from one shore for the first time. They cross each other, touch the opposite bank and return. They meet each other again at 300 ft from the other shore. What is the width of the lake?
  • a)
    2400 ft
  • b)
    1800 ft
  • c)
    2700 ft
  • d)
    3600 ft
Correct answer is option 'A'. Can you explain this answer?

Aditi Kumar answered
Let us assume that the width of the lake = x. So, when one of the runners A covers 900 m, the other one B is covering (x - 900) m. To meet next time, A will be covering (x - 900 + 300) m whereas B will be covering (900 + X-300) m.
Now, 900/(x - 900) = (x - 900 + 300)/(x + 900 - 300)
Now use options to find the answer.

Manish travels a certain distance by car at the rate of 12 km/h and walks back at the rate of 3km/h. The whole journey took 5 hours. What is the distance he covered on the car?
  • a)
    12 km
  • b)
    30 km
  • c)
    15 km
  • d)
    6 km
Correct answer is option 'A'. Can you explain this answer?

You can solve this question using the options. Option (a) fits the given situation best as if we take
the distance as 12 km he would have taken 1 hour to go by car and 4 hours to come back walking
—a total of 5 hours as given in the problem.

Distance between Lucknow and Patna is 300 km. Mayank leaves at a speed of x km/h from Lucknow towards Patna. After three hours Sharat leaves at the speed of (x + 10) km/h from Lucknow towards Patna. If x and the number of hours taken to meet after Sharat starts are integers, how much distance can Mayank cover before they meet?
  • a)
    174 km
  • b)
    60 km
  • c)
    150 km
  • d)
    180 km
Correct answer is option 'B'. Can you explain this answer?

One of the ways of solving this question is going through equations. But after a certain stages we will be required to start assuming the values because all the data are not given.
Another way of doing this problem is: Start working by assuming some values. Let us assume the speed of Mayank =10 km/h. In three hours he has covered 30 km. Now Sharat starts with a speed of 20 km/h. He will take 3 hours to meet Mayank. Till that time, the total distance covered by Mayank = 60 km.

It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. What is the ratio of the speed of the train to that of the car?
  • a)
    3 : 4
  • b)
    2 : 3
  • c)
    1 : 2
  • d)
    1 : 3
Correct answer is option 'A'. Can you explain this answer?

Aspire Academy answered
Eight hours for a 600 km journey, when 120 km is done by train and 480 km by car.
It takes 20 minutes more if 200 km is done by train and 400 km by car.
Formula used:
Speed = Distance/Time
Calculation:
Let the speed of the train be x km/h
And the speed of the car be y km/h
⇒ 120/x + 480/y = 8
⇒ 120(1/x + 4/y) = 8
⇒ 1/x + 4/y = 1/15     ...i)
In the second condition
⇒ Total time = 8 + 20/60 = 25/3 hr
∴  200/x + 400/y = 25/3
⇒ 200(1/x + 2/y) = 25/3
⇒ 1/x + 2/y = 1/24     ...ii)
After solving equation (i) and (ii)
(By substracting equation 2 from equation 1)
⇒ x = 60 km/h
⇒ y = 80 km/h
Ratio of the speed of train and car is
⇒ 60 : 80
⇒ 3 : 4
∴ The ratio of the speed of train and car is 3 : 4.

It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. What is the ratio of the speed of the train to that of the car?
  • a)
    3 : 4
  • b)
    2 : 3
  • c)
    1 : 2
  • d)
    1 : 3
Correct answer is option 'A'. Can you explain this answer?

Arya Roy answered
Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120/x + 480/y=8      1/x + 4/y = 1/15 ...(i)
And, 200/x + 400/y = 25/3  1/x + 2/y = 1/24   ...(ii)
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4.

A person going from Pondicherry to Ootacamond travels 120 km by steamer, 450 km by rail and 60 km by horse transit. The journey occupies 13 hours 30 minutes, and the speed of the train is three times that of the horse-transit and 1(1/2) times that of the steamer. Find the speed of the train.
  • a)
    20 kmph
  • b)
    60 kmph
  • c)
    10 kmph
  • d)
    50 kmph
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Given data:
Total distance travelled = 120 km + 450 km + 60 km = 630 km
Total time taken = 13 hours 30 minutes = 13.5 hours

Let the speed of the steamer be x kmph.
Then, the speed of the horse transit = x/1.5 = 2x/3 kmph (as given, the speed of the train is 1.5 times that of the steamer)
And, the speed of the train = 2x kmph (as given, the speed of the train is three times that of the horse-transit)

Calculation:
Let's assume the time taken by the steamer, train, and horse transit are t1, t2, and t3 respectively.
Then, we have:
t1 + t2 + t3 = 13.5 hours - - - (1) (Total time taken)
t1 = 120/x - - - (2) (Time taken by steamer = Distance/Speed)
t2 = 450/2x - - - (3) (Time taken by train = Distance/Speed)
t3 = 60/(2x/3) = 90/x - - - (4) (Time taken by horse transit = Distance/Speed)

Substituting the values of t1, t2, and t3 in equation (1), we get:
120/x + 450/2x + 90/x = 13.5
Simplifying this equation, we get:
x = 60 kmph

Therefore, the speed of the train is 2x = 120 kmph.
Hence, the correct option is (b) 60 kmph.

A wall clock gains 2 minutes in 12 hours, while a table clock loses 2 minutes in 36 hours; bothare set right at noon on Tuesday. The correct time when they both show the same time next would be
  • a)
    12:30 night
  • b)
    12 noon
  • c)
    1:30 night
  • d)
    12 night
Correct answer is option 'B'. Can you explain this answer?

Sagnik Malik answered
In 36 hours, there would be a gap of 8 minutes. The two watches would show the same time when
the gap would be exactly 12 hours or 720 minutes.
The no. of 36 hour time frames required to create this gap = 720/8 = 90.
Total time = 90 × 36 = 3240 hours. Since this is divisible by 24, the watches would show 12
noon.

A motor car does a journey in 17.5 hours, covering the first half at 30 km/h and the second half at 40 km/h. Find the distance of the journey.
  • a)
    684 km
  • b)
    600 km
  • c)
    120 km
  • d)
    540 km
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Given information:
- A motor car does a journey in 17.5 hours.
- The first half of the journey is covered at 30 km/h.
- The second half of the journey is covered at 40 km/h.

To find:
- The distance of the journey.

Solution:
Let the distance of the journey be 'd' km.
Let the time taken to cover the first half of the journey be 't1' hours.
Let the time taken to cover the second half of the journey be 't2' hours.

From the given information, we know the following:
- t1 + t2 = 17.5 (total time taken)
- t1 = d/2 ÷ 30 = d/60 (distance = speed × time)
- t2 = d/2 ÷ 40 = d/80

Substituting t1 and t2 in the first equation, we get:
d/60 + d/80 = 17.5
(4d + 3d)/240 = 17.5
7d = 17.5 × 240
d = 600 km

Therefore, the distance of the journey is 600 km, which is option B.

Note: The solution could be simplified by using the concept of harmonic mean, which gives the average speed of the entire journey as:
2/(1/30 + 1/40) = 2 × 1200/70 = 480/7 km/h
Using the formula distance = speed × time, we get:
distance = (480/7) × 17.5 = 600 km

Walking 6/7th of his usual speed, a man is 12 minutes too late. What is the usual time taken by him to cover that distance?
  • a)
    1 hr 42 min
  • b)
    1 hr
  • c)
    2 hr
  • d)
    1 hr 12 min
Correct answer is option 'D'. Can you explain this answer?

Kavya Sharma answered
New speed = (6/7) of usual speed.
New time = (7/6) of usual time.
Therefore (7/6 of usual time)- (usual time) = (1/5) hr.
=> (1/6 of usual time)= (1/5) hr 
=> usual time = (6/5) hr 
= 1 hr 12 min.

If Arun had walked 1 km/h faster, he would have taken 10 minutes less to walk 2 kilometre. What is Arun’s speed of walking?
  • a)
    1 kmph
  • b)
    2 kmph
  • c)
    3 kmph
  • d)
    6 kmph
Correct answer is option 'C'. Can you explain this answer?

Solve through options using trial and error. For usual speed 3 kmph we have:
Normal time Æ 2/3 hours = 40 minutes.
At 4 kmph the time would be 2/4 hrs, this gives us a distance of 10 minutes. Hence option (c) is
correct.

A merchant can buy goods at the rate of Rs. 20 per good. The particular good is part of an overall collection and the value is linked to the number of items that are already on the market. So, the merchant sells the first good for Rs. 2, second one for Rs. 4, third for Rs. 6…and so on. If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell?
    • a)
      9
    • b)
      16
    • c)
      27
    • d)
      36
    Correct answer is option 'C'. Can you explain this answer?

    Rajeev Kumar answered
    Let us assume he buys n goods.
    Total CP = 20n
    Total SP = 2 + 4 + 6 + 8 ….n terms
    Total SP should be at least 40% more than total CP
    2 + 4 + 6 + 8 ….n terms ≥ 1.4 * 20 n
    2 (1 + 2 + 3 + ….n terms) ≥ 28n
    n(n + 1) ≥ 28n
    n2 + n ≥ 28n
    n2 - 27n ≥ 0
    n ≥ 27
    The question is " If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell?"
    He should sell a minimum of 27 goods.
    Hence, the answer is 27.
    Choice C is the correct answer.

    Two men A and B walk from P to Q, a distance of 21 km, at 3 and 4 km an hour respectively. B reaches Q, returns immediately and meets A at R. The distance from P to R is
    • a)
      12 km
    • b)
      18 km
    • c)
      10 km
    • d)
      24 km
    Correct answer is option 'B'. Can you explain this answer?

    Solution:

    Let's break down the problem step by step:
    1. Time taken by A and B to reach Q:
    - Speed of A = 3 km/hr
    - Speed of B = 4 km/hr
    - Distance = 21 km
    - Time taken by A = Distance/Speed = 21/3 = 7 hours
    - Time taken by B = Distance/Speed = 21/4 = 5.25 hours
    2. Meeting point R:
    - When B reaches Q, he immediately returns towards P.
    - By the time B reaches R, A would have covered a distance of 21 km.
    - Since B takes 5.25 hours to reach Q and back, A covers 3 km/hr x 5.25 hrs = 15.75 km by the time they meet at R.
    - Remaining distance from R to Q covered by B = 21 - 15.75 = 5.25 km
    3. Calculating distance from P to R:
    - Total distance from P to Q = 21 km
    - Distance covered by A when B reaches Q = 21 km
    - Distance covered by B from Q to R = 5.25 km
    - Therefore, distance from P to R = 21 - 5.25 = 15.75 km
    Hence, the distance from P to R is 15.75 km, which is closest to option B (18 km).

    In covering a distance of 30 km, Arun takes 2 hours more than Anil. If Arun doubles his speed, then he would take 1 hour less than Anil. What is Arun's speed?
    • a)
      8 kmph
    • b)
      5 kmph
    • c)
      4 kmph
    • d)
      7 kmph
    Correct answer is option 'B'. Can you explain this answer?

    If Arun doubles his speed, he needs 3 hour less. Double speed means half time. Hence, half of the time required by Arun to cover 30 km = 3 hours

    i.e., Time required by Arun to cover 30 km = 6 hours

    Arun's speed = 30/6 = 5 km/h 

    A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 40 seconds. What is the length of the train in meters?
    • a)
      1777 m
    • b)
      1822 m
    • c)
      400 m
    • d)
      1400 m
    Correct answer is option 'C'. Can you explain this answer?

    Ananya Patel answered
    Given information:
    - Speed of train = 100 kmph
    - Speed of motorbike = 64 kmph
    - Time taken to overtake = 40 seconds

    Calculating relative speed:
    - Relative speed = (100 - 64) kmph = 36 kmph
    - Convert relative speed to m/s: 36 kmph = 10 m/s

    Calculating distance covered in 40 seconds:
    - Distance = Speed x Time
    - Distance = 10 m/s x 40 s = 400 meters

    Length of the train:
    - The distance covered includes the length of the train and the motorbike
    - Let's assume the length of the train is 'x' meters
    - Distance covered by the train = Distance covered by motorbike + Length of the train
    - 400 = 64 x (40/3600) + x
    - 400 = 7.11 + x
    - x = 392.89 meters
    Therefore, the length of the train is approximately 400 meters (option 'C').

    Two athletes cover the same distance at the rate of 10 and 15 kmph respectively. Find the distance travelled when one takes 15 minutes longer than the other.
    • a)
      8.5 km
    • b)
      750 km
    • c)
      7.5 km
    • d)
      15 km
    Correct answer is option 'C'. Can you explain this answer?

    Rajeev Kumar answered
    The distance travelled is 7.5 km.
    Let the time taken by the athlete travelling at 10 kmph be t hours.
    The time taken by the athlete travelling at 15 kmph is t -15/60 hours.
    The distance travelled by both athletes is the same.
    Therefore, 10t = 15(t -15/60)
    Solving for t, we get t = 3/4 hours.
    The distance travelled by both athletes is 10t = 10 * 3/4 = 7.5 km.

    Narayan Murthy walking at a speed of 20 km/h reaches his college 10 minutes late. Next time he increases his speed by 5 km/h, but finds that he is still late by 4 minutes. What is the distance ofhis college from his house?
    • a)
      20 km
    • b)
      6 km
    • c)
      12 km
    • d)
      None of these
    Correct answer is option 'D'. Can you explain this answer?

    Disha Banerjee answered
    By increasing his speed by 25%, he will reduce his time by 20%. (This corresponds to a 6 minute
    drop in his time for travel—since he goes from being 10 minutes late to only 4 minutes late.)
    Hence, his time originally must have been 30 minutes. Hence, the required distance is 20 kmph ×
    0.5 hours = 10 km.

    A man goes to his office from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming, what is the distance between his house and office?
    • a)
      3km
    • b)
      4km
    • c)
      5km
    • d)
      6km
    Correct answer is option 'D'. Can you explain this answer?

    If a car covers a certain distance at x kmph and an equal distance at y kmph,
    the average speed of the whole journey = 2xy/x+y kmph
    Hence, average speed = 2*3*2/2+3 = 12/5 km/hr
    Total time taken = 5hours
    ⇒ Distance travelled = 12/5*5 = 12 km
    ⇒ Distance between his house and office = 12/2 =  6km

    A distance is covered at a certain speed in a certain time. If the double of this distance is covered in four times the time, then what is the ratio of the two speeds?
    • a)
      1.5 : 0.7
    • b)
      1 : 1.9
    • c)
      4 : 2
    • d)
      6 : 1
    Correct answer is option 'C'. Can you explain this answer?

    Upsc Toppers answered
    Case I : Distance D Speed S1 Time D/S1
    Case II : Distance 2D Speed S2 Time 4(D/S1)
    => Speed for case II = S2 = Distance/Time = 2D/(4D/S1) = S1/22/(4/1) = 1/2
    Hence, speed for case I : speed for case II = S1:S= 1:1/2 = 2:1 => Option C is correct.

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