Time and Distance- Aptitude Questions and Answers

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A boy goes to school at the speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in all, the distance of school is: (in km)?

A)
6

B)
7

C)
8

D)
9


Correct Answer :

6


Explanation :

Let the distance is x.then
Time to go to school + Time taken in return = 5
x/3 + x/2 = 5
2x+3x / 6 = 5
5x = 30
So ditance of school is , x = 6 km

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The speed of Karan is 40 kmph and the speed of Arjun is 60 kmph. What is the ratio of time taken by each to cover the same distance?

A)
3 : 2

B)
2 : 3

C)
1 : 2

D)
4:3


Correct Answer :

3: 2


Explanation :

karan cover a km distance in 1/40 hour and Arjun take 1/60 hour
Hence ratio of time taken by karan and arjun would be 60/40 =3/2

A person can reach a place in 50 days by walking and resting for 9 hours a day. If he doubles his speed and also rests for double time then in how many days will he cover the double distance?

A)
126

B)
128

C)
125

D)
129


Correct Answer :

125


Explanation :

he walk = 24 - 9 = 15 hours per day
so the total time he walks would be = 15 * 50 = 750 hours

let the speed is s,distance is d and time is t.
t = d/s = 750 hours
he doubles his speed(2*s) and will cover the double distance(2*d), then new time would still be same i.e.=2*d/2*s=d/s=750 hours

he rests twice more than he did before, so he would walk = 24 - (2*9) = 6 hours per day

So,Required number of days = 750/6 = 125 days

Walking at 3/4 of her normal speed Malleshwari takes 2 hours more than the normal time to reach the destination. What is her normal time?

A)
4 hours

B)
5 hours

C)
6 hours

D)
8 hours


Correct Answer :

6 hours


Explanation :

Distance(d)=Speed(S)*Time(t)
Let the Speed is s and Time is t

distance coverd by Malleshwari in both case is equal.then
s * t = (3/4) * s *(t + 2)
t = (3/4) * (t + 2)
t - 3*t/4 = 3/2
t/4 = 3/2
t = 6

Rahul runs a distance of 1500 m in 5 minutes. What is his speed in Km/hr ?

A)
16 km/hr

B)
18 km/hr

C)
15 km/hr

D)
20 km/hr


Correct Answer :

18 km/hr


Explanation :

Speed(S) = Distance(d)/Time(t)
= 1500/ 5 m/mins
= 300 m/mins
= 300 * (60/1000 ) km/hr
= 18 km/hr

In how many minutes will Rohit cover a distance of 800 m, if he runs at speed of 10 km/hr?

A)
5 min 12 sec

B)
4 min 40 sec

C)
5 min

D)
4 min 48 sec


Correct Answer :

4 min 48 sec


Explanation :

Speed(S) = Distance(d)/Time(t)
Rohit's speed = 10 Km/hr = (10 * 5/18) m/sec = 50/18 m/sec

Time taken to cover 800 m = 800 / (50/18) sec = 800 *18 / 50 sec = 288 sec = 4 min 48 sec

Vinay cover two-third of a certain distance at 4 km/hr and the remaining at 5 km/hr. If he takes 42 minutes in all, the distance is?

A)
2.5 km

B)
4.6 km

C)
4 km

D)
3 km


Correct Answer :

3 km


Explanation :

Speed(S) = Distance(d)/Time(t)
Let total distance be d km.
Then , (2d / 3) / 4 + ( d / 3) / 5 = 42/60
d/6 + d/ 15 = 7/10
5d + 2d = 21
hence, Required distance d = 3 km

A man goes uphill with an average speed of 35 km/hr, and covers down with an average speed of 45 km/hr. The distance travelled in both the cases being the same , the average speed for the entire journey is ?

A)
315/8 km/hr

B)
325/8 km/hr

C)
40 km/hr

D)
315 km/hr


Correct Answer :

315/8 km/hr


Explanation :

When d1 = d2 , Average speed = 2*S1*S2/(S1+S2), where S1 and S2 are the speeds for covering d1 and d2 respectively

Average speed = ( 2*35*45) / (35 + 45) km/hr. = 3150 / 80 = 315 / 8 km/hr

Everyday Ramesh walks to his office at a speed of 2 km/hr and returns at a speed of 3 km/hr. If he takes 5 hours in his to and fro journey, how far is his office from his home?

A)
12 Kms

B)
6 Kms

C)
5 Kms

D)
3 Kms


Correct Answer :

6 Kms


Explanation :

Let distance between his house and office be x km
Time taken to go to office =x/2 hr
Time taken to return =x/3 hr

x/2 + x/3=5
2x+3x=30
5x=30
x=6

i.e., distance between house and office = 6 km

In 30 km distance, Abhay takes two hours more than Sameer. If Abhay will double his speed, then he will take less than 1 hour from Sameer. What is the speed of Abhay (in km / hour)?

A)
5

B)
6

C)
7

D)
8


Correct Answer :

5


Explanation :

Let Abhay's speed be X km/hr and Sameer's speed be Y km/hr
As is given, Abhay takes 2 hours more than Sameer
30/X - 30/Y = 2 ........ (i)

Abhay doubles his speed, i.e his speed becomes 2x, then he would take 1 hour less than Sameer
30/Y - 30/2X = 1 ......... (ii)

After adding above equations
30/X - 30/2X = 3
30/2X=3
X = 5 km/h

The ratio of the speed of two cars is 5 : 4. So, what is the ratio of their time to cover the same distance?

A)
5 : 4

B)
6 : 4

C)
6 : 5

D)
4 : 5


Correct Answer :

4 : 5


Explanation :

Speed(s) = Distance(d)/Time(t)
T1 =D/5
T2=D/4
T1/T2 = 4 / 5

To cover a distance of 315 km in 2.8 hours what should be the average speed of the car?

A)

112.5 m/s


B)

56.25 m/s


C)

62.5 m/s


D)

31.25 m/s



Correct Answer :

31.25 m/s


Explanation :

Total distance = 315 km = 315000 m
Total time = 2.8 * 60 * 60 sec
Average speed = Total distance/Total time
= 315000/2.8 * 60 * 60
= 31.25 m/s

A thief is spotted by a policeman from a distacne of 100 m. When the policeman starts the chase, the thief also starts running. If the speed of the theif is 8 km / hour and that of the policeman is 10 km/hour, then how far will the theif have to run before he is overtaken?

A)

200 m


B)

300 m


C)

400 m


D)

500 m



Correct Answer :

400 m


Explanation :

Let us assume that the time to taken by the policeman to catch the thief is t.
Now, distance run by police in time, t = t*10

Time is same for the thief and policeman.

According to question, 10t = 8t + 100/1000 km
2t = 0.1
t = 0.05

Distance run by thief in 0.05 Hrs =8*0.05 km = 0.4 km = 400 m

Starting from the same point at the same time, Ruhan and Yuvan had to reach the same destination. While Ruhan drove at 45 km/hr, Yuvan was slower by 5 km/hr. If Yuvan arrived at the destination an hour after Ruhan did, the distance covered by each, in Kilometres, was ?

A)
180

B)
420

C)
225

D)
360


Correct Answer :

360


Explanation :

Let the distance is X km , Speed= Distance/Time

Time taken to travel by Ruhan = X/45

Yuvan speed = 5 km/hr slower than Ruhan= 45 - 5 km/hr = 40 km/hr

Time taken to travel by Yuvan = X/40

As is given, X/40 - X/45 = 1 (an hour)

(9*X - 8*X) / 360 = 1

X = 360

While going form A to B, Rahman drove at 40 km an hour but while coming back he drove at only 24 km an hour. what was the average speed (in km/hr) at which he drove ?

A)
30

B)
31

C)
32

D)
33


Correct Answer :

30


Explanation :

When d1 = d2 , Average speed = 2S1S2/(S1+S2), where S1 and S2 are the speeds for covering d1 and d2 respectively

Average speed = 2S1S2/(S1+S2) = 2*40*24/(40+24)= 30 km/hr

How many minutes does a car take to cover a distance of 200 m, if it runs at a speed of 60 kmph?

A)
1/3 minutes

B)
1/5 minutes

C)
1/6 minutes

D)
1/8 minutes


Correct Answer :

1/5 minutes


Explanation :

Time taken to cover 60 km = 1 hour
that is 60000 m = 60 minutes (1 km=1000 m,1 hour=60 minutes)
Time taken to cover 1 m = 60/60000 minutes = 1/1000 minutes
Time taken to cover 200 m = 200 * 1/1000 minutes
= 1/5 minutes.

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